Best Known (35, 86, s)-Nets in Base 64
(35, 86, 513)-Net over F64 — Constructive and digital
Digital (35, 86, 513)-net over F64, using
- t-expansion [i] based on digital (28, 86, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(35, 86, 223497)-Net in Base 64 — Upper bound on s
There is no (35, 86, 223498)-net in base 64, because
- 1 times m-reduction [i] would yield (35, 85, 223498)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3352 056198 002984 262814 424336 257270 087591 022225 499843 176339 773610 549711 810826 329181 758882 459150 412615 358182 944628 038363 153393 076782 956073 362495 715154 442096 > 6485 [i]