Best Known (55−8, 55, s)-Nets in Base 9
(55−8, 55, 1195760)-Net over F9 — Constructive and digital
Digital (47, 55, 1195760)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (42, 50, 1195744)-net over F9, using
- net defined by OOA [i] based on linear OOA(950, 1195744, F9, 8, 8) (dual of [(1195744, 8), 9565902, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(950, 4782976, F9, 8) (dual of [4782976, 4782926, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(950, 4782969, F9, 8) (dual of [4782969, 4782919, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(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(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(950, 4782976, F9, 8) (dual of [4782976, 4782926, 9]-code), using
- net defined by OOA [i] based on linear OOA(950, 1195744, F9, 8, 8) (dual of [(1195744, 8), 9565902, 9]-NRT-code), using
- digital (1, 5, 16)-net over F9, using
(55−8, 55, 2097150)-Net in Base 9 — Constructive
(47, 55, 2097150)-net in base 9, using
- 91 times duplication [i] based on (46, 54, 2097150)-net in base 9, using
- base change [i] based on digital (28, 36, 2097150)-net over F27, using
- net defined by OOA [i] based on linear OOA(2736, 2097150, F27, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2736, 8388600, F27, 8) (dual of [8388600, 8388564, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2736, 8388600, F27, 8) (dual of [8388600, 8388564, 9]-code), using
- net defined by OOA [i] based on linear OOA(2736, 2097150, F27, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- base change [i] based on digital (28, 36, 2097150)-net over F27, using
(55−8, 55, large)-Net over F9 — Digital
Digital (47, 55, large)-net over F9, using
- 91 times duplication [i] based on digital (46, 54, large)-net over F9, using
(55−8, 55, large)-Net in Base 9 — Upper bound on s
There is no (47, 55, large)-net in base 9, because
- 6 times m-reduction [i] would yield (47, 49, large)-net in base 9, but