Best Known (81−30, 81, s)-Nets in Base 64
(81−30, 81, 690)-Net over F64 — Constructive and digital
Digital (51, 81, 690)-net over F64, using
- 2 times m-reduction [i] based on digital (51, 83, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 60, 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
- digital (7, 23, 177)-net over F64, using
- (u, u+v)-construction [i] based on
(81−30, 81, 4369)-Net in Base 64 — Constructive
(51, 81, 4369)-net in base 64, using
- 1 times m-reduction [i] based on (51, 82, 4369)-net in base 64, using
- net defined by OOA [i] based on OOA(6482, 4369, S64, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(6482, 65536, S64, 31), using
- discarding factors based on OA(6482, 65538, S64, 31), using
- discarding parts of the base [i] based on linear OA(25661, 65538, F256, 31) (dual of [65538, 65477, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(25661, 65538, F256, 31) (dual of [65538, 65477, 32]-code), using
- discarding factors based on OA(6482, 65538, S64, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(6482, 65536, S64, 31), using
- net defined by OOA [i] based on OOA(6482, 4369, S64, 31, 31), using
(81−30, 81, 20556)-Net over F64 — Digital
Digital (51, 81, 20556)-net over F64, using
(81−30, 81, large)-Net in Base 64 — Upper bound on s
There is no (51, 81, large)-net in base 64, because
- 28 times m-reduction [i] would yield (51, 53, large)-net in base 64, but