Best Known (22, 22+12, s)-Nets in Base 64
(22, 22+12, 43691)-Net over F64 — Constructive and digital
Digital (22, 34, 43691)-net over F64, using
- net defined by OOA [i] based on linear OOA(6434, 43691, F64, 12, 12) (dual of [(43691, 12), 524258, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
(22, 22+12, 131073)-Net over F64 — Digital
Digital (22, 34, 131073)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6434, 131073, F64, 2, 12) (dual of [(131073, 2), 262112, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- OOA 2-folding [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
(22, 22+12, large)-Net in Base 64 — Upper bound on s
There is no (22, 34, large)-net in base 64, because
- 10 times m-reduction [i] would yield (22, 24, large)-net in base 64, but