Best Known (71−22, 71, s)-Nets in Base 64
(71−22, 71, 23834)-Net over F64 — Constructive and digital
Digital (49, 71, 23834)-net over F64, using
- net defined by OOA [i] based on linear OOA(6471, 23834, F64, 22, 22) (dual of [(23834, 22), 524277, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6471, 262174, F64, 22) (dual of [262174, 262103, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6471, 262175, F64, 22) (dual of [262175, 262104, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(647, 31, F64, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(6471, 262175, F64, 22) (dual of [262175, 262104, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6471, 262174, F64, 22) (dual of [262174, 262103, 23]-code), using
(71−22, 71, 262175)-Net over F64 — Digital
Digital (49, 71, 262175)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6471, 262175, F64, 22) (dual of [262175, 262104, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(647, 31, F64, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
(71−22, 71, large)-Net in Base 64 — Upper bound on s
There is no (49, 71, large)-net in base 64, because
- 20 times m-reduction [i] would yield (49, 51, large)-net in base 64, but