Best Known (12−11, 12, s)-Nets in Base 64
(12−11, 12, 80)-Net over F64 — Constructive and digital
Digital (1, 12, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
(12−11, 12, 81)-Net over F64 — Digital
Digital (1, 12, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
(12−11, 12, 387)-Net in Base 64 — Upper bound on s
There is no (1, 12, 388)-net in base 64, because
- 1 times m-reduction [i] would yield (1, 11, 388)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 74 691265 944524 727520 > 6411 [i]