Information on Result #1707608
Digital (36, 41, 1594338)-net over F3, using net defined by OOA based on linear OOA(341, 1594338, F3, 5, 5) (dual of [(1594338, 5), 7971649, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(341, 1594338, F3, 4, 5) (dual of [(1594338, 4), 6377311, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(341, 1594338, F3, 5) (dual of [1594338, 1594297, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(327, 1594323, F3, 4) (dual of [1594323, 1594296, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(4) ⊂ Ce(3) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(341, 1594338, F3, 5) (dual of [1594338, 1594297, 6]-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.