Best Known (47−12, 47, s)-Nets in Base 64
(47−12, 47, 1398100)-Net over F64 — Constructive and digital
Digital (35, 47, 1398100)-net over F64, using
- 642 times duplication [i] based on digital (33, 45, 1398100)-net over F64, using
- net defined by OOA [i] based on linear OOA(6445, 1398100, F64, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6445, 8388600, F64, 12) (dual of [8388600, 8388555, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6445, 8388600, F64, 12) (dual of [8388600, 8388555, 13]-code), using
- net defined by OOA [i] based on linear OOA(6445, 1398100, F64, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
(47−12, 47, large)-Net over F64 — Digital
Digital (35, 47, large)-net over F64, using
- 641 times duplication [i] based on digital (34, 46, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6446, large, F64, 12) (dual of [large, large−46, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 1 times code embedding in larger space [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6446, large, F64, 12) (dual of [large, large−46, 13]-code), using
(47−12, 47, large)-Net in Base 64 — Upper bound on s
There is no (35, 47, large)-net in base 64, because
- 10 times m-reduction [i] would yield (35, 37, large)-net in base 64, but