Best Known (66, 66+∞, s)-Nets in Base 5
(66, 66+∞, 82)-Net over F5 — Constructive and digital
Digital (66, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(66, 66+∞, 120)-Net over F5 — Digital
Digital (66, m, 120)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 119)-sequence over F5, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 61 and N(F) ≥ 120, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
(66, 66+∞, 281)-Net in Base 5 — Upper bound on s
There is no (66, m, 282)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (66, 1123, 282)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51123, 282, S5, 4, 1057), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 53 097031 790719 412787 429142 441424 177839 490493 472437 024009 998534 153160 086983 276552 331024 760355 900187 283455 857148 472151 725686 285905 284006 428108 025011 096508 733790 673050 286581 684485 182591 861471 592084 728086 073897 387861 124642 905583 993719 515024 088608 620616 964775 894281 508639 204532 655292 889545 993989 925266 096960 053863 746319 888848 305592 945797 722303 686723 997133 143392 468475 680798 740311 568478 577024 880282 546611 112064 161714 432585 698716 479780 726650 285332 466440 686316 250548 771344 606464 546008 975135 846406 013963 443577 995034 997420 804802 481213 167564 042924 300650 646695 887403 358364 759274 863064 394035 406415 875033 199970 862377 730069 248456 228355 064352 006468 206097 558100 216583 848961 470484 823990 802201 464006 948839 446388 356851 962323 579285 731191 454508 620049 714976 288702 099360 174158 082514 850320 876576 006412 506103 515625 / 529 > 51123 [i]
- extracting embedded OOA [i] would yield OOA(51123, 282, S5, 4, 1057), but