Best Known (145−25, 145, s)-Nets in Base 9
(145−25, 145, 44297)-Net over F9 — Constructive and digital
Digital (120, 145, 44297)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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 (108, 133, 44287)-net over F9, using
- net defined by OOA [i] based on linear OOA(9133, 44287, F9, 25, 25) (dual of [(44287, 25), 1107042, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9133, 531445, F9, 25) (dual of [531445, 531312, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 531447, F9, 25) (dual of [531447, 531314, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 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(24) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9133, 531447, F9, 25) (dual of [531447, 531314, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9133, 531445, F9, 25) (dual of [531445, 531312, 26]-code), using
- net defined by OOA [i] based on linear OOA(9133, 44287, F9, 25, 25) (dual of [(44287, 25), 1107042, 26]-NRT-code), using
- digital (0, 12, 10)-net over F9, using
(145−25, 145, 713666)-Net over F9 — Digital
Digital (120, 145, 713666)-net over F9, using
(145−25, 145, large)-Net in Base 9 — Upper bound on s
There is no (120, 145, large)-net in base 9, because
- 23 times m-reduction [i] would yield (120, 122, large)-net in base 9, but