Best Known (50, 60, s)-Nets in Base 9
(50, 60, 956597)-Net over F9 — Constructive and digital
Digital (50, 60, 956597)-net over F9, using
- net defined by OOA [i] based on linear OOA(960, 956597, F9, 10, 10) (dual of [(956597, 10), 9565910, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(960, 4782985, F9, 10) (dual of [4782985, 4782925, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(960, 4782986, F9, 10) (dual of [4782986, 4782926, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(93, 17, F9, 2) (dual of [17, 14, 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(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(960, 4782986, F9, 10) (dual of [4782986, 4782926, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(960, 4782985, F9, 10) (dual of [4782985, 4782925, 11]-code), using
(50, 60, 4782986)-Net over F9 — Digital
Digital (50, 60, 4782986)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(960, 4782986, F9, 10) (dual of [4782986, 4782926, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(93, 17, F9, 2) (dual of [17, 14, 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(9) ⊂ Ce(6) [i] based on
(50, 60, large)-Net in Base 9 — Upper bound on s
There is no (50, 60, large)-net in base 9, because
- 8 times m-reduction [i] would yield (50, 52, large)-net in base 9, but