Best Known (87−10, 87, s)-Nets in Base 9
(87−10, 87, 3358680)-Net over F9 — Constructive and digital
Digital (77, 87, 3358680)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 3240)-net over F9, using
- net defined by OOA [i] based on linear OOA(913, 3240, F9, 5, 5) (dual of [(3240, 5), 16187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(913, 6481, F9, 5) (dual of [6481, 6468, 6]-code), using
- net defined by OOA [i] based on linear OOA(913, 3240, F9, 5, 5) (dual of [(3240, 5), 16187, 6]-NRT-code), using
- digital (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on 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
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- digital (8, 13, 3240)-net over F9, using
(87−10, 87, large)-Net over F9 — Digital
Digital (77, 87, large)-net over F9, using
- t-expansion [i] based on digital (76, 87, large)-net over F9, using
- 2 times m-reduction [i] based on digital (76, 89, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- 2 times m-reduction [i] based on digital (76, 89, large)-net over F9, using
(87−10, 87, large)-Net in Base 9 — Upper bound on s
There is no (77, 87, large)-net in base 9, because
- 8 times m-reduction [i] would yield (77, 79, large)-net in base 9, but