Best Known (23−6, 23, s)-Nets in Base 81
(23−6, 23, 2796201)-Net over F81 — Constructive and digital
Digital (17, 23, 2796201)-net over F81, using
- 812 times duplication [i] based on digital (15, 21, 2796201)-net over F81, using
- net defined by OOA [i] based on linear OOA(8121, 2796201, F81, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(8121, 2796201, F81, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
(23−6, 23, large)-Net over F81 — Digital
Digital (17, 23, large)-net over F81, using
- 812 times duplication [i] based on digital (15, 21, large)-net over F81, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
(23−6, 23, large)-Net in Base 81 — Upper bound on s
There is no (17, 23, large)-net in base 81, because
- 4 times m-reduction [i] would yield (17, 19, large)-net in base 81, but