Best Known (8, 8+97, s)-Nets in Base 16
(8, 8+97, 65)-Net over F16 — Constructive and digital
Digital (8, 105, 65)-net over F16, using
- t-expansion [i] based on digital (6, 105, 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
(8, 8+97, 224)-Net in Base 16 — Upper bound on s
There is no (8, 105, 225)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16105, 225, S16, 97), but
- the linear programming bound shows that M ≥ 96 480638 741603 112728 303754 051930 697813 756878 827422 019489 590181 311555 336469 274677 802538 057898 676110 462427 589416 810800 218183 570941 507295 203704 083167 425067 096496 043923 862866 631101 576247 030886 449046 145148 472514 249278 619648 / 34 460548 829084 349297 069291 595246 557440 647871 421704 869537 866958 120450 609264 527162 670401 653305 > 16105 [i]