Best Known (37−27, 37, s)-Nets in Base 32
(37−27, 37, 104)-Net over F32 — Constructive and digital
Digital (10, 37, 104)-net over F32, using
- t-expansion [i] based on digital (9, 37, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
(37−27, 37, 113)-Net over F32 — Digital
Digital (10, 37, 113)-net over F32, using
- net from sequence [i] based on digital (10, 112)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 10 and N(F) ≥ 113, using
(37−27, 37, 2686)-Net in Base 32 — Upper bound on s
There is no (10, 37, 2687)-net in base 32, because
- 1 times m-reduction [i] would yield (10, 36, 2687)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 539451 224427 188985 533647 122947 476247 199474 234669 163790 > 3236 [i]