Best Known (54, 82, s)-Nets in Base 64
(54, 82, 18724)-Net over F64 — Constructive and digital
Digital (54, 82, 18724)-net over F64, using
- net defined by OOA [i] based on linear OOA(6482, 18724, F64, 28, 28) (dual of [(18724, 28), 524190, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
(54, 82, 97277)-Net over F64 — Digital
Digital (54, 82, 97277)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6482, 97277, F64, 2, 28) (dual of [(97277, 2), 194472, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6482, 131073, F64, 2, 28) (dual of [(131073, 2), 262064, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6482, 262146, F64, 28) (dual of [262146, 262064, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 262147, F64, 28) (dual of [262147, 262065, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(27) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(6482, 262147, F64, 28) (dual of [262147, 262065, 29]-code), using
- OOA 2-folding [i] based on linear OA(6482, 262146, F64, 28) (dual of [262146, 262064, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(6482, 131073, F64, 2, 28) (dual of [(131073, 2), 262064, 29]-NRT-code), using
(54, 82, large)-Net in Base 64 — Upper bound on s
There is no (54, 82, large)-net in base 64, because
- 26 times m-reduction [i] would yield (54, 56, large)-net in base 64, but