Best Known (47, 47+11, s)-Nets in Base 9
(47, 47+11, 106291)-Net over F9 — Constructive and digital
Digital (47, 58, 106291)-net over F9, using
- net defined by OOA [i] based on linear OOA(958, 106291, F9, 11, 11) (dual of [(106291, 11), 1169143, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(958, 531456, F9, 11) (dual of [531456, 531398, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(93, 15, F9, 2) (dual of [15, 12, 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(10) ⊂ Ce(7) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(958, 531456, F9, 11) (dual of [531456, 531398, 12]-code), using
(47, 47+11, 531456)-Net over F9 — Digital
Digital (47, 58, 531456)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(958, 531456, F9, 11) (dual of [531456, 531398, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(93, 15, F9, 2) (dual of [15, 12, 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(10) ⊂ Ce(7) [i] based on
(47, 47+11, large)-Net in Base 9 — Upper bound on s
There is no (47, 58, large)-net in base 9, because
- 9 times m-reduction [i] would yield (47, 49, large)-net in base 9, but