Best Known (42−39, 42, s)-Nets in Base 16
(42−39, 42, 38)-Net over F16 — Constructive and digital
Digital (3, 42, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
(42−39, 42, 148)-Net in Base 16 — Upper bound on s
There is no (3, 42, 149)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1642, 149, S16, 39), but
- the linear programming bound shows that M ≥ 5195 481312 093501 228795 805423 209591 318667 403140 917012 422952 657771 720041 562112 / 13 081795 668111 509405 874727 > 1642 [i]