Best Known (3, 12, s)-Nets in Base 16
(3, 12, 38)-Net over F16 — Constructive and digital
Digital (3, 12, 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
(3, 12, 299)-Net in Base 16 — Upper bound on s
There is no (3, 12, 300)-net in base 16, because
- 1 times m-reduction [i] would yield (3, 11, 300)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1611, 300, S16, 8), but
- the linear programming bound shows that M ≥ 1 872782 507099 708293 382144 / 106215 735659 > 1611 [i]
- extracting embedded orthogonal array [i] would yield OA(1611, 300, S16, 8), but