Best Known (75−15, 75, s)-Nets in Base 9
(75−15, 75, 8456)-Net over F9 — Constructive and digital
Digital (60, 75, 8456)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (51, 66, 8436)-net over F9, using
- net defined by OOA [i] based on linear OOA(966, 8436, F9, 15, 15) (dual of [(8436, 15), 126474, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(966, 59053, F9, 15) (dual of [59053, 58987, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(966, 59054, F9, 15) (dual of [59054, 58988, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(966, 59049, F9, 15) (dual of [59049, 58983, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(966, 59054, F9, 15) (dual of [59054, 58988, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(966, 59053, F9, 15) (dual of [59053, 58987, 16]-code), using
- net defined by OOA [i] based on linear OOA(966, 8436, F9, 15, 15) (dual of [(8436, 15), 126474, 16]-NRT-code), using
- digital (2, 9, 20)-net over F9, using
(75−15, 75, 97816)-Net over F9 — Digital
Digital (60, 75, 97816)-net over F9, using
(75−15, 75, large)-Net in Base 9 — Upper bound on s
There is no (60, 75, large)-net in base 9, because
- 13 times m-reduction [i] would yield (60, 62, large)-net in base 9, but