Best Known (68−40, 68, s)-Nets in Base 64
(68−40, 68, 513)-Net over F64 — Constructive and digital
Digital (28, 68, 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
(68−40, 68, 182370)-Net in Base 64 — Upper bound on s
There is no (28, 68, 182371)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 661 103606 179585 506546 909051 110324 339940 078635 567625 959106 021347 267381 497361 078351 731089 017164 313320 480671 179327 620481 307496 > 6468 [i]