Best Known (77−48, 77, s)-Nets in Base 64
(77−48, 77, 513)-Net over F64 — Constructive and digital
Digital (29, 77, 513)-net over F64, using
- t-expansion [i] based on digital (28, 77, 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
(77−48, 77, 97005)-Net in Base 64 — Upper bound on s
There is no (29, 77, 97006)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 11 909960 356418 451700 764939 216215 028869 887859 031481 987245 227866 908087 047616 903263 266799 855950 151660 806680 317827 561283 634695 840125 640014 279594 > 6477 [i]