Best Known (23−12, 23, s)-Nets in Base 64
(23−12, 23, 683)-Net over F64 — Constructive and digital
Digital (11, 23, 683)-net over F64, using
- net defined by OOA [i] based on linear OOA(6423, 683, F64, 12, 12) (dual of [(683, 12), 8173, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 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
- OA 6-folding and stacking [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
(23−12, 23, 1366)-Net over F64 — Digital
Digital (11, 23, 1366)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6423, 1366, F64, 3, 12) (dual of [(1366, 3), 4075, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 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
- OOA 3-folding [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
(23−12, 23, 398628)-Net in Base 64 — Upper bound on s
There is no (11, 23, 398629)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 348450 510997 751790 663397 866021 511856 376592 > 6423 [i]