Best Known (14, 14+8, s)-Nets in Base 64
(14, 14+8, 65536)-Net over F64 — Constructive and digital
Digital (14, 22, 65536)-net over F64, using
- net defined by OOA [i] based on linear OOA(6422, 65536, F64, 8, 8) (dual of [(65536, 8), 524266, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using
(14, 14+8, 131073)-Net over F64 — Digital
Digital (14, 22, 131073)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6422, 131073, F64, 2, 8) (dual of [(131073, 2), 262124, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6422, 262146, F64, 8) (dual of [262146, 262124, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(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(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- OOA 2-folding [i] based on linear OA(6422, 262146, F64, 8) (dual of [262146, 262124, 9]-code), using
(14, 14+8, large)-Net in Base 64 — Upper bound on s
There is no (14, 22, large)-net in base 64, because
- 6 times m-reduction [i] would yield (14, 16, large)-net in base 64, but