Best Known (32, 46, s)-Nets in Base 64
(32, 46, 37453)-Net over F64 — Constructive and digital
Digital (32, 46, 37453)-net over F64, using
- net defined by OOA [i] based on linear OOA(6446, 37453, F64, 14, 14) (dual of [(37453, 14), 524296, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6446, 262171, F64, 14) (dual of [262171, 262125, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
- 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(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(13) ⊂ Ce(6) [i] based on
- OA 7-folding and stacking [i] based on linear OA(6446, 262171, F64, 14) (dual of [262171, 262125, 15]-code), using
(32, 46, 262171)-Net over F64 — Digital
Digital (32, 46, 262171)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6446, 262171, F64, 14) (dual of [262171, 262125, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
- 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(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(13) ⊂ Ce(6) [i] based on
(32, 46, large)-Net in Base 64 — Upper bound on s
There is no (32, 46, large)-net in base 64, because
- 12 times m-reduction [i] would yield (32, 34, large)-net in base 64, but