Best Known (90−82, 90, s)-Nets in Base 16
(90−82, 90, 65)-Net over F16 — Constructive and digital
Digital (8, 90, 65)-net over F16, using
- t-expansion [i] based on digital (6, 90, 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
(90−82, 90, 294)-Net in Base 16 — Upper bound on s
There is no (8, 90, 295)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1690, 295, S16, 82), but
- the linear programming bound shows that M ≥ 1 670457 139451 272670 071497 784913 765604 440868 717481 667565 684939 591768 804749 748063 229060 788657 484521 825639 788934 740537 938775 799384 836801 792219 461347 195392 741776 722452 662212 950490 436216 683495 424000 / 696677 276012 947560 560710 886791 457899 595163 764343 122053 868961 251241 483334 173787 977743 > 1690 [i]