Best Known (119−27, 119, s)-Nets in Base 9
(119−27, 119, 1019)-Net over F9 — Constructive and digital
Digital (92, 119, 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 (79, 106, 1009)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 1009, F9, 27, 27) (dual of [(1009, 27), 27137, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9106, 13118, F9, 27) (dual of [13118, 13012, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 13124, F9, 27) (dual of [13124, 13018, 28]-code), using
- trace code [i] based on linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- trace code [i] based on linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 13124, F9, 27) (dual of [13124, 13018, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9106, 13118, F9, 27) (dual of [13118, 13012, 28]-code), using
- net defined by OOA [i] based on linear OOA(9106, 1009, F9, 27, 27) (dual of [(1009, 27), 27137, 28]-NRT-code), using
- digital (0, 13, 10)-net over F9, using
(119−27, 119, 1514)-Net in Base 9 — Constructive
(92, 119, 1514)-net in base 9, using
- 91 times duplication [i] based on (91, 118, 1514)-net in base 9, using
- net defined by OOA [i] based on OOA(9118, 1514, S9, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(9118, 19683, S9, 27), using
- 1 times code embedding in larger space [i] based on OA(9117, 19682, S9, 27), using
- discarding parts of the base [i] based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- 1 times truncation [i] based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 1 times truncation [i] based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- discarding parts of the base [i] based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- 1 times code embedding in larger space [i] based on OA(9117, 19682, S9, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(9118, 19683, S9, 27), using
- net defined by OOA [i] based on OOA(9118, 1514, S9, 27, 27), using
(119−27, 119, 30752)-Net over F9 — Digital
Digital (92, 119, 30752)-net over F9, using
(119−27, 119, large)-Net in Base 9 — Upper bound on s
There is no (92, 119, large)-net in base 9, because
- 25 times m-reduction [i] would yield (92, 94, large)-net in base 9, but