Best Known (63, 63+26, s)-Nets in Base 64
(63, 63+26, 20230)-Net over F64 — Constructive and digital
Digital (63, 89, 20230)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (50, 76, 20165)-net over F64, using
- net defined by OOA [i] based on linear OOA(6476, 20165, F64, 26, 26) (dual of [(20165, 26), 524214, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(6476, 262145, F64, 26) (dual of [262145, 262069, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(6476, 262145, F64, 26) (dual of [262145, 262069, 27]-code), using
- net defined by OOA [i] based on linear OOA(6476, 20165, F64, 26, 26) (dual of [(20165, 26), 524214, 27]-NRT-code), using
- digital (0, 13, 65)-net over F64, using
(63, 63+26, 161319)-Net in Base 64 — Constructive
(63, 89, 161319)-net in base 64, using
- net defined by OOA [i] based on OOA(6489, 161319, S64, 26, 26), using
- OA 13-folding and stacking [i] based on OA(6489, 2097147, S64, 26), using
- discarding factors based on OA(6489, 2097155, S64, 26), using
- discarding parts of the base [i] based on linear OA(12876, 2097155, F128, 26) (dual of [2097155, 2097079, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(12876, 2097152, F128, 26) (dual of [2097152, 2097076, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(12876, 2097155, F128, 26) (dual of [2097155, 2097079, 27]-code), using
- discarding factors based on OA(6489, 2097155, S64, 26), using
- OA 13-folding and stacking [i] based on OA(6489, 2097147, S64, 26), using
(63, 63+26, 434809)-Net over F64 — Digital
Digital (63, 89, 434809)-net over F64, using
(63, 63+26, large)-Net in Base 64 — Upper bound on s
There is no (63, 89, large)-net in base 64, because
- 24 times m-reduction [i] would yield (63, 65, large)-net in base 64, but