Best Known (35, 35+10, s)-Nets in Base 81
(35, 35+10, 1680960)-Net over F81 — Constructive and digital
Digital (35, 45, 1680960)-net over F81, using
- 811 times duplication [i] based on digital (34, 44, 1680960)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 3240)-net over F81, using
- net defined by OOA [i] based on linear OOA(817, 3240, F81, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(817, 3240, F81, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- appending kth column [i] based on linear OOA(817, 3240, F81, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(817, 3240, F81, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
- digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- digital (2, 7, 3240)-net over F81, using
- (u, u+v)-construction [i] based on
(35, 35+10, large)-Net over F81 — Digital
Digital (35, 45, large)-net over F81, using
- t-expansion [i] based on digital (33, 45, large)-net over F81, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
(35, 35+10, large)-Net in Base 81 — Upper bound on s
There is no (35, 45, large)-net in base 81, because
- 8 times m-reduction [i] would yield (35, 37, large)-net in base 81, but