Best Known (1, 1+41, s)-Nets in Base 64
(1, 1+41, 80)-Net over F64 — Constructive and digital
Digital (1, 42, 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
(1, 1+41, 81)-Net over F64 — Digital
Digital (1, 42, 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
(1, 1+41, 386)-Net in Base 64 — Upper bound on s
There is no (1, 42, 387)-net in base 64, because
- 29 times m-reduction [i] would yield (1, 13, 387)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 303643 134427 673040 438880 > 6413 [i]