Best Known (46−7, 46, s)-Nets in Base 9
(46−7, 46, 1594335)-Net over F9 — Constructive and digital
Digital (39, 46, 1594335)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (36, 43, 1594325)-net over F9, using
- net defined by OOA [i] based on linear OOA(943, 1594325, F9, 7, 7) (dual of [(1594325, 7), 11160232, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(943, 4782976, F9, 7) (dual of [4782976, 4782933, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- 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(936, 4782969, F9, 6) (dual of [4782969, 4782933, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(943, 4782976, F9, 7) (dual of [4782976, 4782933, 8]-code), using
- net defined by OOA [i] based on linear OOA(943, 1594325, F9, 7, 7) (dual of [(1594325, 7), 11160232, 8]-NRT-code), using
- digital (0, 3, 10)-net over F9, using
(46−7, 46, 7744466)-Net over F9 — Digital
Digital (39, 46, 7744466)-net over F9, using
(46−7, 46, large)-Net in Base 9 — Upper bound on s
There is no (39, 46, large)-net in base 9, because
- 5 times m-reduction [i] would yield (39, 41, large)-net in base 9, but