Best Known (61, 61+15, s)-Nets in Base 9
(61, 61+15, 8464)-Net over F9 — Constructive and digital
Digital (61, 76, 8464)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-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 (3, 10, 28)-net over F9, using
(61, 61+15, 114437)-Net over F9 — Digital
Digital (61, 76, 114437)-net over F9, using
(61, 61+15, large)-Net in Base 9 — Upper bound on s
There is no (61, 76, large)-net in base 9, because
- 13 times m-reduction [i] would yield (61, 63, large)-net in base 9, but