Best Known (79−20, 79, s)-Nets in Base 81
(79−20, 79, 838860)-Net over F81 — Constructive and digital
Digital (59, 79, 838860)-net over F81, using
- 812 times duplication [i] based on digital (57, 77, 838860)-net over F81, using
- net defined by OOA [i] based on linear OOA(8177, 838860, F81, 20, 20) (dual of [(838860, 20), 16777123, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8177, 8388600, F81, 20) (dual of [8388600, 8388523, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8177, large, F81, 20) (dual of [large, large−77, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(8177, large, F81, 20) (dual of [large, large−77, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8177, 8388600, F81, 20) (dual of [8388600, 8388523, 21]-code), using
- net defined by OOA [i] based on linear OOA(8177, 838860, F81, 20, 20) (dual of [(838860, 20), 16777123, 21]-NRT-code), using
(79−20, 79, large)-Net over F81 — Digital
Digital (59, 79, large)-net over F81, using
- 812 times duplication [i] based on digital (57, 77, large)-net over F81, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8177, large, F81, 20) (dual of [large, large−77, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8177, large, F81, 20) (dual of [large, large−77, 21]-code), using
(79−20, 79, large)-Net in Base 81 — Upper bound on s
There is no (59, 79, large)-net in base 81, because
- 18 times m-reduction [i] would yield (59, 61, large)-net in base 81, but