Best Known (34, 34+54, s)-Nets in Base 64
(34, 34+54, 513)-Net over F64 — Constructive and digital
Digital (34, 88, 513)-net over F64, using
- t-expansion [i] based on digital (28, 88, 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
(34, 34+54, 133607)-Net in Base 64 — Upper bound on s
There is no (34, 88, 133608)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 878 753374 781975 070101 856019 523556 216649 548944 129398 180554 486821 585581 373907 047717 727686 629290 040348 071313 041187 957312 688654 963287 851603 045377 436993 975118 180588 > 6488 [i]