Best Known (58−52, 58, s)-Nets in Base 16
(58−52, 58, 65)-Net over F16 — Constructive and digital
Digital (6, 58, 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
(58−52, 58, 283)-Net in Base 16 — Upper bound on s
There is no (6, 58, 284)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1658, 284, S16, 52), but
- the linear programming bound shows that M ≥ 2702 746347 707741 524812 796821 244425 249599 708844 145722 782741 688066 689912 234068 819918 517092 379409 682750 966937 419776 / 383132 652625 124589 645468 838793 658895 437691 > 1658 [i]