Information on Result #1208139
Digital (137, 150, 1398831)-net over F3, using (u, u+v)-construction based on
- digital (23, 29, 731)-net over F3, using
- net defined by OOA [i] based on linear OOA(329, 731, F3, 6, 6) (dual of [(731, 6), 4357, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(329, 731, F3, 5, 6) (dual of [(731, 5), 3626, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(329, 2193, F3, 6) (dual of [2193, 2164, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(329, 2195, F3, 6) (dual of [2195, 2166, 7]-code), using
- 1 times truncation [i] based on linear OA(330, 2196, F3, 7) (dual of [2196, 2166, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(38, 9, F3, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
- dual of repetition code with length 9 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- 1 times truncation [i] based on linear OA(330, 2196, F3, 7) (dual of [2196, 2166, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(329, 2195, F3, 6) (dual of [2195, 2166, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(329, 2193, F3, 6) (dual of [2193, 2164, 7]-code), using
- appending kth column [i] based on linear OOA(329, 731, F3, 5, 6) (dual of [(731, 5), 3626, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(329, 731, F3, 6, 6) (dual of [(731, 6), 4357, 7]-NRT-code), using
- digital (108, 121, 1398100)-net over F3, using
- net defined by OOA [i] based on linear OOA(3121, 1398100, F3, 13, 13) (dual of [(1398100, 13), 18175179, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3121, 8388601, F3, 13) (dual of [8388601, 8388480, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3121, 8388601, F3, 13) (dual of [8388601, 8388480, 14]-code), using
- net defined by OOA [i] based on linear OOA(3121, 1398100, F3, 13, 13) (dual of [(1398100, 13), 18175179, 14]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.