Best Known (126, 126+22, s)-Nets in Base 9
(126, 126+22, 434844)-Net over F9 — Constructive and digital
Digital (126, 148, 434844)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- 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
- net defined by OOA [i] based on linear OOA(9134, 434816, F9, 22, 22) (dual of [(434816, 22), 9565818, 23]-NRT-code), using
- digital (3, 14, 28)-net over F9, using
(126, 126+22, 5761573)-Net over F9 — Digital
Digital (126, 148, 5761573)-net over F9, using
(126, 126+22, large)-Net in Base 9 — Upper bound on s
There is no (126, 148, large)-net in base 9, because
- 20 times m-reduction [i] would yield (126, 128, large)-net in base 9, but