Best Known (37, ∞, s)-Nets in Base 8
(37, ∞, 98)-Net over F8 — Constructive and digital
Digital (37, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(37, ∞, 121)-Net over F8 — Digital
Digital (37, m, 121)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(37, ∞, 281)-Net in Base 8 — Upper bound on s
There is no (37, m, 282)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (37, 842, 282)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8842, 282, S8, 3, 805), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 693870 086488 835189 009780 678312 256021 296210 581692 605750 948219 758922 316024 789222 879475 157692 343019 529661 946153 917364 676469 720306 742426 336953 609912 886701 662401 153925 182316 237658 955200 610239 039619 370071 813691 391396 836969 857344 497949 373170 378398 036517 994874 440506 777442 622484 213674 969392 448325 026618 570211 718523 496813 182347 533870 846404 764368 526614 822574 459400 274268 803155 158117 478826 556112 026108 507432 192614 836108 714691 739826 328222 451119 745274 215391 823747 959432 035272 594414 995637 485373 372080 049478 552240 162346 759185 054128 093196 382751 230317 190735 141231 099740 471097 599497 663575 319927 026566 648811 968712 865236 422771 824640 976990 528580 776342 856435 651093 267121 402779 762247 542456 921358 124231 024084 695851 293459 586176 075575 239203 448159 199104 640480 301771 105304 541739 275660 558336 / 403 > 8842 [i]
- extracting embedded OOA [i] would yield OOA(8842, 282, S8, 3, 805), but