The density of minimal size single-insertion codes of
3 symbols covering all strings of 4 symbols
(N is the number of symbols in the alphabet - assume the symbols are the
digits 1 to N)
N=2 density=0.5 optimal code (there are two): 111 122 211 222
N=3 density=0.4444444444444444 optimal code (there are two): 111 112 121 133 211 222 223 232 313 322 331
333
N=4 density=0.46875 optimal code (there are more than 100): 111 113 114 122 124 131 142 212 214 221 222 224 233 241 242 311 323 332 333 334 343 344 412 421 422 433 434 441 443
444
N=5 density=0.456 optimal code: 111 114 115 122 123 132 133 141 151 154 155 212 213 221 222 223 231 232 244 245 254 255 311 312 321 322 333 334 335 343 344 345 353 411 424 425 433 434 435 442 443 444 445 452 453 511 514 515 524 525 533 541 542 551 552 554
555