Best Known (89, 89+26, s)-Nets in Base 9
(89, 89+26, 1019)-Net over F9 — Constructive and digital
Digital (89, 115, 1019)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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 (76, 102, 1009)-net over F9, using
- net defined by OOA [i] based on linear OOA(9102, 1009, F9, 26, 26) (dual of [(1009, 26), 26132, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9102, 13117, F9, 26) (dual of [13117, 13015, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9102, 13117, F9, 26) (dual of [13117, 13015, 27]-code), using
- net defined by OOA [i] based on linear OOA(9102, 1009, F9, 26, 26) (dual of [(1009, 26), 26132, 27]-NRT-code), using
- digital (0, 13, 10)-net over F9, using
(89, 89+26, 1514)-Net in Base 9 — Constructive
(89, 115, 1514)-net in base 9, using
- 91 times duplication [i] based on (88, 114, 1514)-net in base 9, using
- base change [i] based on digital (50, 76, 1514)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- base change [i] based on digital (50, 76, 1514)-net over F27, using
(89, 89+26, 31205)-Net over F9 — Digital
Digital (89, 115, 31205)-net over F9, using
(89, 89+26, large)-Net in Base 9 — Upper bound on s
There is no (89, 115, large)-net in base 9, because
- 24 times m-reduction [i] would yield (89, 91, large)-net in base 9, but