Best Known (112, 112+26, s)-Nets in Base 9
(112, 112+26, 4583)-Net over F9 — Constructive and digital
Digital (112, 138, 4583)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 21, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (91, 117, 4543)-net over F9, using
- net defined by OOA [i] based on linear OOA(9117, 4543, F9, 26, 26) (dual of [(4543, 26), 118001, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9117, 59059, F9, 26) (dual of [59059, 58942, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9117, 59060, F9, 26) (dual of [59060, 58943, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9117, 59060, F9, 26) (dual of [59060, 58943, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9117, 59059, F9, 26) (dual of [59059, 58942, 27]-code), using
- net defined by OOA [i] based on linear OOA(9117, 4543, F9, 26, 26) (dual of [(4543, 26), 118001, 27]-NRT-code), using
- digital (8, 21, 40)-net over F9, using
(112, 112+26, 235493)-Net over F9 — Digital
Digital (112, 138, 235493)-net over F9, using
(112, 112+26, large)-Net in Base 9 — Upper bound on s
There is no (112, 138, large)-net in base 9, because
- 24 times m-reduction [i] would yield (112, 114, large)-net in base 9, but