Best Known (53, 53+13, s)-Nets in Base 9
(53, 53+13, 9887)-Net over F9 — Constructive and digital
Digital (53, 66, 9887)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 45)-net over F9, using
- digital (43, 56, 9842)-net over F9, using
- net defined by OOA [i] based on linear OOA(956, 9842, F9, 13, 13) (dual of [(9842, 13), 127890, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(956, 59053, F9, 13) (dual of [59053, 58997, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 59054, F9, 13) (dual of [59054, 58998, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(956, 59054, F9, 13) (dual of [59054, 58998, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(956, 59053, F9, 13) (dual of [59053, 58997, 14]-code), using
- net defined by OOA [i] based on linear OOA(956, 9842, F9, 13, 13) (dual of [(9842, 13), 127890, 14]-NRT-code), using
(53, 53+13, 117119)-Net over F9 — Digital
Digital (53, 66, 117119)-net over F9, using
(53, 53+13, large)-Net in Base 9 — Upper bound on s
There is no (53, 66, large)-net in base 9, because
- 11 times m-reduction [i] would yield (53, 55, large)-net in base 9, but