Best Known (8, ∞, s)-Nets in Base 27
(8, ∞, 84)-Net over F27 — Constructive and digital
Digital (8, m, 84)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
(8, ∞, 92)-Net over F27 — Digital
Digital (8, m, 92)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (8, 91)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 92, using
(8, ∞, 252)-Net in Base 27 — Upper bound on s
There is no (8, m, 253)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (8, 251, 253)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27251, 253, S27, 243), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 271939 452626 362232 031719 277774 080120 944104 211366 463680 718737 338316 927093 380917 117791 557877 121162 318194 798049 474899 587568 385301 716677 576368 973311 278834 063664 308006 116742 099439 517205 790962 357904 601112 541950 157779 802478 959115 833315 857730 535984 373859 074295 052788 436509 469459 582652 129141 951374 703891 698741 314798 750715 215077 901516 842836 438094 323628 570572 954921 227605 / 122 > 27251 [i]
- extracting embedded OOA [i] would yield OA(27251, 253, S27, 243), but