Best Known (59, 59+20, s)-Nets in Base 64
(59, 59+20, 838860)-Net over F64 — Constructive and digital
Digital (59, 79, 838860)-net over F64, using
- 642 times duplication [i] based on digital (57, 77, 838860)-net over F64, using
- net defined by OOA [i] based on linear OOA(6477, 838860, F64, 20, 20) (dual of [(838860, 20), 16777123, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(6477, 8388600, F64, 20) (dual of [8388600, 8388523, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(6477, 8388600, F64, 20) (dual of [8388600, 8388523, 21]-code), using
- net defined by OOA [i] based on linear OOA(6477, 838860, F64, 20, 20) (dual of [(838860, 20), 16777123, 21]-NRT-code), using
(59, 59+20, 8045795)-Net over F64 — Digital
Digital (59, 79, 8045795)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6479, 8045795, F64, 20) (dual of [8045795, 8045716, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6479, large, F64, 20) (dual of [large, large−79, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 2 times code embedding in larger space [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6479, large, F64, 20) (dual of [large, large−79, 21]-code), using
(59, 59+20, large)-Net in Base 64 — Upper bound on s
There is no (59, 79, large)-net in base 64, because
- 18 times m-reduction [i] would yield (59, 61, large)-net in base 64, but