Best Known (85, 95, s)-Nets in Base 9
(85, 95, 3384966)-Net over F9 — Constructive and digital
Digital (85, 95, 3384966)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (16, 21, 29526)-net over F9, using
- net defined by OOA [i] based on linear OOA(921, 29526, F9, 5, 5) (dual of [(29526, 5), 147609, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(921, 59053, F9, 5) (dual of [59053, 59032, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(921, 59054, F9, 5) (dual of [59054, 59033, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(921, 59049, F9, 5) (dual of [59049, 59028, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(916, 59049, F9, 4) (dual of [59049, 59033, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(921, 59054, F9, 5) (dual of [59054, 59033, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(921, 59053, F9, 5) (dual of [59053, 59032, 6]-code), using
- net defined by OOA [i] based on linear OOA(921, 29526, F9, 5, 5) (dual of [(29526, 5), 147609, 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 (16, 21, 29526)-net over F9, using
(85, 95, large)-Net over F9 — Digital
Digital (85, 95, large)-net over F9, using
- t-expansion [i] based on digital (83, 95, large)-net over F9, using
- 2 times m-reduction [i] based on digital (83, 97, large)-net over F9, using
(85, 95, large)-Net in Base 9 — Upper bound on s
There is no (85, 95, large)-net in base 9, because
- 8 times m-reduction [i] would yield (85, 87, large)-net in base 9, but