Best Known (106, s)-Sequences in Base 3
(106, 72)-Sequence over F3 — Constructive and digital
Digital (106, 72)-sequence over F3, using
- base reduction for sequences [i] based on digital (17, 72)-sequence over F9, using
- s-reduction based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- s-reduction based on digital (17, 73)-sequence over F9, using
(106, 103)-Sequence over F3 — Digital
Digital (106, 103)-sequence over F3, using
- t-expansion [i] based on digital (102, 103)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 102 and N(F) ≥ 104, using
(106, 224)-Sequence in Base 3 — Upper bound on s
There is no (106, 225)-sequence in base 3, because
- net from sequence [i] would yield (106, m, 226)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (106, 1123, 226)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31123, 226, S3, 5, 1017), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37525 364226 809373 817770 636870 312419 841614 154099 836924 388847 008161 233264 483972 043007 397848 600873 138244 142646 485057 080004 496493 729743 571398 990705 985510 042630 015217 890476 851808 290851 807458 494080 256764 629699 485476 144976 013206 359276 468900 307670 856170 374982 715744 143559 649064 283591 855829 874015 185250 551826 502902 149249 251109 356672 866983 907282 470149 757118 787135 583904 543640 352205 222449 073953 526982 344003 697134 113391 142970 386318 785262 349008 710409 962907 632221 667788 119432 408851 999187 824003 826330 223750 834930 516315 650190 738834 086400 397844 325785 503795 / 509 > 31123 [i]
- extracting embedded OOA [i] would yield OOA(31123, 226, S3, 5, 1017), but
- m-reduction [i] would yield (106, 1123, 226)-net in base 3, but