Best Known (30, 63, s)-Nets in Base 64
(30, 63, 513)-Net over F64 — Constructive and digital
Digital (30, 63, 513)-net over F64, using
- t-expansion [i] based on digital (28, 63, 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
(30, 63, 793)-Net over F64 — Digital
Digital (30, 63, 793)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6463, 793, F64, 33) (dual of [793, 730, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(6463, 819, F64, 33) (dual of [819, 756, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 819 | 642−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(6463, 819, F64, 33) (dual of [819, 756, 34]-code), using
(30, 63, 1076818)-Net in Base 64 — Upper bound on s
There is no (30, 63, 1076819)-net in base 64, because
- 1 times m-reduction [i] would yield (30, 62, 1076819)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 9619 723553 817745 602250 312634 055729 140353 556965 997820 512626 420110 389994 912252 247127 530601 067739 755722 788086 418501 > 6462 [i]