Best Known (120, ∞, s)-Nets in Base 3
(120, ∞, 77)-Net over F3 — Constructive and digital
Digital (120, m, 77)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (120, 76)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 76)-sequence over F9, using
- s-reduction 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
- s-reduction based on digital (22, 77)-sequence over F9, using
- base reduction for sequences [i] based on digital (22, 76)-sequence over F9, using
(120, ∞, 120)-Net over F3 — Digital
Digital (120, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (120, 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
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(120, ∞, 253)-Net in Base 3 — Upper bound on s
There is no (120, m, 254)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (120, 1517, 254)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31517, 254, S3, 6, 1397), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 868572 294879 409541 790179 268465 289849 668738 757954 264285 683429 864068 063283 013302 253313 391582 370992 368442 870470 437240 797172 534962 623373 381804 014551 781498 796834 293458 036174 913425 070643 950602 333595 715839 464641 416229 383387 677993 150219 243936 155402 820102 866024 253320 192664 895960 363259 308278 058811 738898 245421 737654 304418 848879 160861 518134 226599 617706 889893 969625 054295 748915 449040 174398 229340 775670 306313 244016 129253 179356 103082 588698 613722 248567 269570 149344 248094 601308 276902 937592 846853 188005 486000 019263 468617 980867 023240 924154 597706 059785 287735 817449 002561 574080 090667 533097 322684 739780 449039 429368 593901 820972 284451 656339 975369 142132 377508 044229 624788 446627 633628 672863 119998 938168 547566 677033 358466 780281 107784 037479 087009 479063 / 233 > 31517 [i]
- extracting embedded OOA [i] would yield OOA(31517, 254, S3, 6, 1397), but