Best Known (37−25, 37, s)-Nets in Base 4
(37−25, 37, 28)-Net over F4 — Constructive and digital
Digital (12, 37, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
(37−25, 37, 29)-Net over F4 — Digital
Digital (12, 37, 29)-net over F4, using
- net from sequence [i] based on digital (12, 28)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 29, using
(37−25, 37, 103)-Net in Base 4 — Upper bound on s
There is no (12, 37, 104)-net in base 4, because
- 1 times m-reduction [i] would yield (12, 36, 104)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 4912 251607 372428 372340 > 436 [i]