Best Known (126, s)-Sequences in Base 3
(126, 77)-Sequence over F3 — Constructive and digital
Digital (126, 77)-sequence over F3, using
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
(126, 119)-Sequence over F3 — Digital
Digital (126, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(126, 264)-Sequence in Base 3 — Upper bound on s
There is no (126, 265)-sequence in base 3, because
- net from sequence [i] would yield (126, m, 266)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (126, 1589, 266)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31589, 266, S3, 6, 1463), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20838 191170 795476 985380 777309 440607 284962 594720 561662 801073 968100 348909 770600 173118 596673 495047 679937 791326 579740 451517 578322 779457 598285 622786 929633 536736 587033 842440 983138 909162 212424 029034 110094 857842 545165 062911 560376 717836 458149 287525 342357 432780 390025 264648 022371 628202 593898 492831 491957 153015 420127 882432 692674 495821 442535 011446 218080 557812 128730 509586 062919 811044 055975 307760 459083 944861 250128 069011 276447 425486 119025 930655 066060 185998 282098 317863 618746 580590 135778 862411 886240 144136 886981 132008 572844 618771 127962 762834 693946 178408 891122 310626 554023 360022 570990 531920 954314 307966 634180 871429 824759 734400 696357 635186 493979 811271 876662 147149 203961 232663 091066 906308 262280 273898 628164 006874 760178 530966 008237 199748 427005 608911 562325 063050 531923 803632 001967 / 122 > 31589 [i]
- extracting embedded OOA [i] would yield OOA(31589, 266, S3, 6, 1463), but
- m-reduction [i] would yield (126, 1589, 266)-net in base 3, but