Best Known (50, 50+26, s)-Nets in Base 64
(50, 50+26, 20165)-Net over F64 — Constructive and digital
Digital (50, 76, 20165)-net over F64, using
- net defined by OOA [i] based on linear OOA(6476, 20165, F64, 26, 26) (dual of [(20165, 26), 524214, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(6476, 262145, F64, 26) (dual of [262145, 262069, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(6476, 262145, F64, 26) (dual of [262145, 262069, 27]-code), using
(50, 50+26, 96885)-Net over F64 — Digital
Digital (50, 76, 96885)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6476, 96885, F64, 2, 26) (dual of [(96885, 2), 193694, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6476, 131073, F64, 2, 26) (dual of [(131073, 2), 262070, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6476, 262146, F64, 26) (dual of [262146, 262070, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- OOA 2-folding [i] based on linear OA(6476, 262146, F64, 26) (dual of [262146, 262070, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(6476, 131073, F64, 2, 26) (dual of [(131073, 2), 262070, 27]-NRT-code), using
(50, 50+26, large)-Net in Base 64 — Upper bound on s
There is no (50, 76, large)-net in base 64, because
- 24 times m-reduction [i] would yield (50, 52, large)-net in base 64, but