Best Known (43, 89, s)-Nets in Base 64
(43, 89, 513)-Net over F64 — Constructive and digital
Digital (43, 89, 513)-net over F64, using
- t-expansion [i] based on digital (28, 89, 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
(43, 89, 1102)-Net over F64 — Digital
Digital (43, 89, 1102)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6489, 1102, F64, 46) (dual of [1102, 1013, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(6489, 1366, F64, 46) (dual of [1366, 1277, 47]-code), using
- an extension Ce(45) of the narrow-sense BCH-code C(I) with length 1365 | 642−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- discarding factors / shortening the dual code based on linear OA(6489, 1366, F64, 46) (dual of [1366, 1277, 47]-code), using
(43, 89, 1459632)-Net in Base 64 — Upper bound on s
There is no (43, 89, 1459633)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 56236 783713 369620 055807 042980 261730 540239 035056 988794 017099 850611 348217 786297 635495 854245 569257 852354 126173 975439 471681 713312 524094 763737 641209 360253 408193 172960 > 6489 [i]