Best Known (7, 7+67, s)-Nets in Base 16
(7, 7+67, 65)-Net over F16 — Constructive and digital
Digital (7, 74, 65)-net over F16, using
- t-expansion [i] based on digital (6, 74, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(7, 7+67, 285)-Net in Base 16 — Upper bound on s
There is no (7, 74, 286)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1674, 286, S16, 67), but
- the linear programming bound shows that M ≥ 380 454062 822711 266641 809307 284140 335957 881394 418284 924649 587300 885392 992444 271302 794129 502315 728545 622569 398258 551502 567761 523375 639975 502733 811251 453710 303232 / 2922 385214 331337 004500 733432 529369 075773 144196 901231 759832 643564 841807 > 1674 [i]