Best Known (43, 43+13, s)-Nets in Base 9
(43, 43+13, 9842)-Net over F9 — Constructive and digital
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
(43, 43+13, 36230)-Net over F9 — Digital
Digital (43, 56, 36230)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(956, 36230, F9, 13) (dual of [36230, 36174, 14]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using
(43, 43+13, large)-Net in Base 9 — Upper bound on s
There is no (43, 56, large)-net in base 9, because
- 11 times m-reduction [i] would yield (43, 45, large)-net in base 9, but