Best Known (44, 44+47, s)-Nets in Base 64
(44, 44+47, 513)-Net over F64 — Constructive and digital
Digital (44, 91, 513)-net over F64, using
- t-expansion [i] based on digital (28, 91, 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
(44, 44+47, 1125)-Net over F64 — Digital
Digital (44, 91, 1125)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6491, 1125, F64, 47) (dual of [1125, 1034, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(6491, 1366, F64, 47) (dual of [1366, 1275, 48]-code), using
- an extension Ce(46) of the narrow-sense BCH-code C(I) with length 1365 | 642−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- discarding factors / shortening the dual code based on linear OA(6491, 1366, F64, 47) (dual of [1366, 1275, 48]-code), using
(44, 44+47, 1748935)-Net in Base 64 — Upper bound on s
There is no (44, 91, 1748936)-net in base 64, because
- 1 times m-reduction [i] would yield (44, 90, 1748936)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 599177 103036 930190 362192 761805 185419 205584 130976 957566 955244 647129 247550 186167 261479 554142 629331 527766 637968 555124 076381 496121 840923 540833 319360 116498 206818 971884 > 6490 [i]