Best Known (32, 32+47, s)-Nets in Base 64
(32, 32+47, 513)-Net over F64 — Constructive and digital
Digital (32, 79, 513)-net over F64, using
- t-expansion [i] based on digital (28, 79, 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
(32, 32+47, 199708)-Net in Base 64 — Upper bound on s
There is no (32, 79, 199709)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 78, 199709)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 762 170756 218664 976612 928777 944149 386464 164174 655514 531692 906446 800209 545337 797991 943370 462640 985576 820666 248677 027612 182110 916683 019678 351128 > 6478 [i]