Best Known (70−42, 70, s)-Nets in Base 64
(70−42, 70, 513)-Net over F64 — Constructive and digital
Digital (28, 70, 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
(70−42, 70, 144451)-Net in Base 64 — Upper bound on s
There is no (28, 70, 144452)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2 708037 957741 486981 023267 505170 639271 229824 523934 682437 240600 276984 926971 043894 109031 214164 047961 731826 657383 875636 826780 774992 > 6470 [i]