Information on Result #1713216
Digital (58, 72, 873)-net over F3, using net defined by OOA based on linear OOA(372, 873, F3, 20, 14) (dual of [(873, 20), 17388, 15]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(372, 1747, F3, 4, 14) (dual of [(1747, 4), 6916, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(372, 1748, F3, 4, 14) (dual of [(1748, 4), 6920, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(372, 1748, F3, 14) (dual of [1748, 1676, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(372, 2217, F3, 14) (dual of [2217, 2145, 15]-code), using
- construction XX applied to Ce(13) ⊂ Ce(9) ⊂ Ce(7) [i] based on
- linear OA(364, 2187, F3, 14) (dual of [2187, 2123, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(13) ⊂ Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(372, 2217, F3, 14) (dual of [2217, 2145, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(372, 1748, F3, 14) (dual of [1748, 1676, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(372, 1748, F3, 4, 14) (dual of [(1748, 4), 6920, 15]-NRT-code), using
Mode: 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.