Best Known (51, 51+18, s)-Nets in Base 64
(51, 51+18, 932067)-Net over F64 — Constructive and digital
Digital (51, 69, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
(51, 51+18, 5122270)-Net over F64 — Digital
Digital (51, 69, 5122270)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6469, 5122270, F64, 18) (dual of [5122270, 5122201, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
(51, 51+18, large)-Net in Base 64 — Upper bound on s
There is no (51, 69, large)-net in base 64, because
- 16 times m-reduction [i] would yield (51, 53, large)-net in base 64, but