Best Known (132, ∞, s)-Nets in Base 3
(132, ∞, 78)-Net over F3 — Constructive and digital
Digital (132, m, 78)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 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
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
(132, ∞, 120)-Net over F3 — Digital
Digital (132, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 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
(132, ∞, 277)-Net in Base 3 — Upper bound on s
There is no (132, m, 278)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (132, 1661, 278)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31661, 278, S3, 6, 1529), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 61 963343 831948 000895 995957 407292 496584 450310 196144 286560 055803 100892 737454 429894 198668 101879 228068 315965 295674 014510 411044 205629 100370 775670 698404 723090 515088 341070 774249 203966 234963 699623 472447 219433 236447 454008 023946 238250 110274 400549 163741 949699 313012 630086 950133 149271 658998 362872 836217 383181 608477 450974 704042 564483 972111 017701 216069 489205 286546 067428 096141 591962 948628 710422 504270 202658 439987 370354 561494 189254 719169 196709 847706 344757 231008 951230 629864 049322 211379 751105 675581 202971 706222 955789 717230 208835 378204 609411 466449 472224 617626 250543 971000 006470 740819 584788 346660 885951 247756 779271 101401 085401 907972 031958 488703 702445 545916 866439 507959 723943 487904 827096 270575 357681 966890 536033 479892 360818 836123 369931 988154 565142 233667 630991 740996 986274 444214 283386 996499 793838 541258 508289 926859 / 17 > 31661 [i]
- extracting embedded OOA [i] would yield OOA(31661, 278, S3, 6, 1529), but