Best Known (88−46, 88, s)-Nets in Base 64
(88−46, 88, 513)-Net over F64 — Constructive and digital
Digital (42, 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
(88−46, 88, 975)-Net over F64 — Digital
Digital (42, 88, 975)-net over F64, using
(88−46, 88, 1218185)-Net in Base 64 — Upper bound on s
There is no (42, 88, 1218186)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 878 707417 069271 648664 525689 225546 945411 959667 118395 175866 823653 358825 107326 089358 355651 155253 942572 166458 578506 007842 856013 806177 504842 719378 105246 919306 116384 > 6488 [i]