Best Known (132, 132+∞, s)-Nets in Base 4
(132, 132+∞, 130)-Net over F4 — Constructive and digital
Digital (132, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(132, 132+∞, 176)-Net over F4 — Digital
Digital (132, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(132, 132+∞, 412)-Net in Base 4 — Upper bound on s
There is no (132, m, 413)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (132, 2059, 413)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42059, 413, S4, 5, 1927), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 193682 016131 178805 113924 306527 710690 161103 765725 929349 441194 029775 071225 775650 376741 259811 235191 679710 994331 146637 852271 870167 008015 826322 107323 998019 768185 479331 163073 564008 189519 864263 059180 578644 003455 419528 130592 964644 640922 683606 664275 228727 090160 882806 150215 539032 273309 533973 285631 185487 956931 354681 450182 459838 849285 286398 144709 797531 094657 641209 426169 341200 668161 929995 634511 619928 420248 390673 399294 486084 552057 819576 909012 863712 718950 159667 594903 374848 401519 856422 460695 090019 850886 185945 217067 972390 323111 164808 010909 963296 220289 470321 234999 623109 823333 350811 900942 479616 269299 960581 193968 422954 196934 386986 874511 491298 282750 817666 906711 285397 810687 000435 533305 719532 309999 544920 261249 848661 714784 601829 682461 620304 665334 410254 736854 462577 079962 310285 927053 953583 659031 058157 713265 800952 112902 437445 140074 491460 135185 636783 359556 427500 416755 883101 673433 942050 247186 953928 833069 420221 562660 118738 071751 678848 401525 538777 748362 953449 505421 201818 446395 672097 499440 307545 862450 172627 697197 314831 602221 696004 156732 035767 340825 906459 634198 590657 920354 812179 988922 387508 289835 659056 673595 232731 804396 791080 408564 859145 800311 164344 204772 650707 748057 130489 788110 659111 408971 343174 825026 201514 045178 596761 627122 201664 779493 769811 031480 074240 / 241 > 42059 [i]
- extracting embedded OOA [i] would yield OOA(42059, 413, S4, 5, 1927), but