Best Known (65, 65+22, s)-Nets in Base 64
(65, 65+22, 762600)-Net over F64 — Constructive and digital
Digital (65, 87, 762600)-net over F64, using
- 642 times duplication [i] based on digital (63, 85, 762600)-net over F64, using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
(65, 65+22, 7700857)-Net over F64 — Digital
Digital (65, 87, 7700857)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6487, 7700857, F64, 22) (dual of [7700857, 7700770, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6487, large, F64, 22) (dual of [large, large−87, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 2 times code embedding in larger space [i] based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6487, large, F64, 22) (dual of [large, large−87, 23]-code), using
(65, 65+22, large)-Net in Base 64 — Upper bound on s
There is no (65, 87, large)-net in base 64, because
- 20 times m-reduction [i] would yield (65, 67, large)-net in base 64, but