Best Known (84−46, 84, s)-Nets in Base 64
(84−46, 84, 513)-Net over F64 — Constructive and digital
Digital (38, 84, 513)-net over F64, using
- t-expansion [i] based on digital (28, 84, 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
(84−46, 84, 680)-Net over F64 — Digital
Digital (38, 84, 680)-net over F64, using
(84−46, 84, 591004)-Net in Base 64 — Upper bound on s
There is no (38, 84, 591005)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 52 375340 414908 375808 777529 626476 914682 462221 509891 519175 120257 526928 076628 621844 013034 524513 784832 318370 433651 885516 718929 739585 884834 367905 138689 728216 > 6484 [i]