Best Known (40−37, 40, s)-Nets in Base 16
(40−37, 40, 38)-Net over F16 — Constructive and digital
Digital (3, 40, 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
(40−37, 40, 161)-Net in Base 16 — Upper bound on s
There is no (3, 40, 162)-net in base 16, because
- 5 times m-reduction [i] would yield (3, 35, 162)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1635, 162, S16, 32), but
- the linear programming bound shows that M ≥ 4853 573546 032429 937192 168908 048884 147376 956821 677601 984190 873600 / 3413 823898 487425 614953 > 1635 [i]
- extracting embedded orthogonal array [i] would yield OA(1635, 162, S16, 32), but