Best Known (81−75, 81, s)-Nets in Base 16
(81−75, 81, 65)-Net over F16 — Constructive and digital
Digital (6, 81, 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
(81−75, 81, 205)-Net in Base 16 — Upper bound on s
There is no (6, 81, 206)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1681, 206, S16, 75), but
- the linear programming bound shows that M ≥ 42 706891 792118 933397 834516 274858 607320 735182 661159 087755 032940 280816 659364 714295 118584 736188 877261 101727 255174 704638 739438 974843 722613 902746 320896 / 1 208956 270438 985578 224849 381452 342697 095313 833591 > 1681 [i]