Best Known (124−29, 124, s)-Nets in Base 9
(124−29, 124, 972)-Net over F9 — Constructive and digital
Digital (95, 124, 972)-net over F9, using
- 92 times duplication [i] based on digital (93, 122, 972)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (18, 32, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 16, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 16, 116)-net over F81, using
- digital (61, 90, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 45, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 45, 370)-net over F81, using
- digital (18, 32, 232)-net over F9, using
- (u, u+v)-construction [i] based on
(124−29, 124, 1406)-Net in Base 9 — Constructive
(95, 124, 1406)-net in base 9, using
- 91 times duplication [i] based on (94, 123, 1406)-net in base 9, using
- base change [i] based on digital (53, 82, 1406)-net over F27, using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- base change [i] based on digital (53, 82, 1406)-net over F27, using
(124−29, 124, 23774)-Net over F9 — Digital
Digital (95, 124, 23774)-net over F9, using
(124−29, 124, large)-Net in Base 9 — Upper bound on s
There is no (95, 124, large)-net in base 9, because
- 27 times m-reduction [i] would yield (95, 97, large)-net in base 9, but