Best Known (3, 3+19, s)-Nets in Base 64
(3, 3+19, 104)-Net over F64 — Constructive and digital
Digital (3, 22, 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
(3, 3+19, 113)-Net over F64 — Digital
Digital (3, 22, 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
(3, 3+19, 1074)-Net in Base 64 — Upper bound on s
There is no (3, 22, 1075)-net in base 64, because
- 1 times m-reduction [i] would yield (3, 21, 1075)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 85 506522 544753 941398 768584 065436 359196 > 6421 [i]