Best Known (37−34, 37, s)-Nets in Base 64
(37−34, 37, 104)-Net over F64 — Constructive and digital
Digital (3, 37, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
(37−34, 37, 113)-Net over F64 — Digital
Digital (3, 37, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
(37−34, 37, 951)-Net in Base 64 — Upper bound on s
There is no (3, 37, 952)-net in base 64, because
- 6 times m-reduction [i] would yield (3, 31, 952)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 98 626822 983347 319646 251571 585526 768547 580911 870096 036994 > 6431 [i]