Best Known (134−22, 134, s)-Nets in Base 9
(134−22, 134, 434816)-Net over F9 — Constructive and digital
Digital (112, 134, 434816)-net over F9, using
- net defined by OOA [i] based on linear OOA(9134, 434816, F9, 22, 22) (dual of [(434816, 22), 9565818, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9134, 4782976, F9, 22) (dual of [4782976, 4782842, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9127, 4782969, F9, 21) (dual of [4782969, 4782842, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 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(21) ⊂ Ce(20) [i] based on
- OA 11-folding and stacking [i] based on linear OA(9134, 4782976, F9, 22) (dual of [4782976, 4782842, 23]-code), using
(134−22, 134, 2391488)-Net over F9 — Digital
Digital (112, 134, 2391488)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(9134, 2391488, F9, 2, 22) (dual of [(2391488, 2), 4782842, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9134, 4782976, F9, 22) (dual of [4782976, 4782842, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9127, 4782969, F9, 21) (dual of [4782969, 4782842, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 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(21) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(9134, 4782976, F9, 22) (dual of [4782976, 4782842, 23]-code), using
(134−22, 134, large)-Net in Base 9 — Upper bound on s
There is no (112, 134, large)-net in base 9, because
- 20 times m-reduction [i] would yield (112, 114, large)-net in base 9, but