Best Known (34, 34+8, s)-Nets in Base 9
(34, 34+8, 14799)-Net over F9 — Constructive and digital
Digital (34, 42, 14799)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 36)-net over F9, using
- net defined by OOA [i] based on linear OOA(96, 36, F9, 4, 4) (dual of [(36, 4), 138, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(96, 36, F9, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- appending kth column [i] based on linear OOA(96, 36, F9, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(96, 36, F9, 4, 4) (dual of [(36, 4), 138, 5]-NRT-code), using
- digital (28, 36, 14763)-net over F9, using
- net defined by OOA [i] based on linear OOA(936, 14763, F9, 8, 8) (dual of [(14763, 8), 118068, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(936, 59052, F9, 8) (dual of [59052, 59016, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(936, 59054, F9, 8) (dual of [59054, 59018, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(936, 59054, F9, 8) (dual of [59054, 59018, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(936, 59052, F9, 8) (dual of [59052, 59016, 9]-code), using
- net defined by OOA [i] based on linear OOA(936, 14763, F9, 8, 8) (dual of [(14763, 8), 118068, 9]-NRT-code), using
- digital (2, 6, 36)-net over F9, using
(34, 34+8, 224538)-Net over F9 — Digital
Digital (34, 42, 224538)-net over F9, using
(34, 34+8, large)-Net in Base 9 — Upper bound on s
There is no (34, 42, large)-net in base 9, because
- 6 times m-reduction [i] would yield (34, 36, large)-net in base 9, but