Best Known (56, 56+26, s)-Nets in Base 64
(56, 56+26, 20167)-Net over F64 — Constructive and digital
Digital (56, 82, 20167)-net over F64, using
- net defined by OOA [i] based on linear OOA(6482, 20167, F64, 26, 26) (dual of [(20167, 26), 524260, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [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(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(646, 27, F64, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- OA 13-folding and stacking [i] based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
(56, 56+26, 194023)-Net over F64 — Digital
Digital (56, 82, 194023)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6482, 194023, F64, 26) (dual of [194023, 193941, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [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(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(646, 27, F64, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
(56, 56+26, large)-Net in Base 64 — Upper bound on s
There is no (56, 82, large)-net in base 64, because
- 24 times m-reduction [i] would yield (56, 58, large)-net in base 64, but