Best Known (53, 53+37, s)-Nets in Base 64
(53, 53+37, 690)-Net over F64 — Constructive and digital
Digital (53, 90, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 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, 65, 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, 25, 177)-net over F64, using
(53, 53+37, 910)-Net in Base 64 — Constructive
(53, 90, 910)-net in base 64, using
- 644 times duplication [i] based on (49, 86, 910)-net in base 64, using
- net defined by OOA [i] based on OOA(6486, 910, S64, 37, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(6486, 16381, S64, 37), using
- discarding factors based on OA(6486, 16386, S64, 37), using
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- discarding factors based on OA(6486, 16386, S64, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(6486, 16381, S64, 37), using
- net defined by OOA [i] based on OOA(6486, 910, S64, 37, 37), using
(53, 53+37, 7446)-Net over F64 — Digital
Digital (53, 90, 7446)-net over F64, using
(53, 53+37, large)-Net in Base 64 — Upper bound on s
There is no (53, 90, large)-net in base 64, because
- 35 times m-reduction [i] would yield (53, 55, large)-net in base 64, but