Best Known (46, 46+13, s)-Nets in Base 9
(46, 46+13, 9844)-Net over F9 — Constructive and digital
Digital (46, 59, 9844)-net over F9, using
- net defined by OOA [i] based on linear OOA(959, 9844, F9, 13, 13) (dual of [(9844, 13), 127913, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(959, 59065, F9, 13) (dual of [59065, 59006, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(959, 59067, F9, 13) (dual of [59067, 59008, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [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(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(959, 59067, F9, 13) (dual of [59067, 59008, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(959, 59065, F9, 13) (dual of [59065, 59006, 14]-code), using
(46, 46+13, 59067)-Net over F9 — Digital
Digital (46, 59, 59067)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(959, 59067, F9, 13) (dual of [59067, 59008, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [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(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
(46, 46+13, large)-Net in Base 9 — Upper bound on s
There is no (46, 59, large)-net in base 9, because
- 11 times m-reduction [i] would yield (46, 48, large)-net in base 9, but