Best Known (12, 24, s)-Nets in Base 64
(12, 24, 683)-Net over F64 — Constructive and digital
Digital (12, 24, 683)-net over F64, using
- 641 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(6423, 683, F64, 12, 12) (dual of [(683, 12), 8173, 13]-NRT-code), using
(12, 24, 1708)-Net over F64 — Digital
Digital (12, 24, 1708)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6424, 1708, F64, 2, 12) (dual of [(1708, 2), 3392, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6424, 2050, F64, 2, 12) (dual of [(2050, 2), 4076, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6424, 4100, F64, 12) (dual of [4100, 4076, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6424, 4101, F64, 12) (dual of [4101, 4077, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [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(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(6424, 4101, F64, 12) (dual of [4101, 4077, 13]-code), using
- OOA 2-folding [i] based on linear OA(6424, 4100, F64, 12) (dual of [4100, 4076, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(6424, 2050, F64, 2, 12) (dual of [(2050, 2), 4076, 13]-NRT-code), using
(12, 24, 797260)-Net in Base 64 — Upper bound on s
There is no (12, 24, 797261)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 22 300900 636366 441297 650629 161388 209508 181820 > 6424 [i]