Best Known (98−90, 98, s)-Nets in Base 16
(98−90, 98, 65)-Net over F16 — Constructive and digital
Digital (8, 98, 65)-net over F16, using
- t-expansion [i] based on digital (6, 98, 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
(98−90, 98, 258)-Net in Base 16 — Upper bound on s
There is no (8, 98, 259)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1698, 259, S16, 90), but
- the linear programming bound shows that M ≥ 213928 299979 691122 819318 864262 618529 811411 568876 287955 447450 932452 547497 926684 129682 017872 381109 159994 665487 543645 324973 580719 371834 481606 008668 617754 939972 923614 455244 591300 621761 257729 422087 517713 942672 572416 / 20 679318 934857 615344 425176 996797 999644 801452 227962 843503 178869 610263 380195 308013 551806 130261 > 1698 [i]