Information on Result #1712302
Digital (44, 51, 265727)-net over F3, using net defined by OOA based on linear OOA(351, 265727, F3, 9, 7) (dual of [(265727, 9), 2391492, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(351, 265728, F3, 3, 7) (dual of [(265728, 3), 797133, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(351, 265728, F3, 2, 7) (dual of [(265728, 2), 531405, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(351, 531456, F3, 7) (dual of [531456, 531405, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(350, 531455, F3, 7) (dual of [531455, 531405, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(349, 531441, F3, 7) (dual of [531441, 531392, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(337, 531441, F3, 5) (dual of [531441, 531404, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 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 code embedding in larger space [i] based on linear OA(350, 531455, F3, 7) (dual of [531455, 531405, 8]-code), using
- OOA 2-folding [i] based on linear OA(351, 531456, F3, 7) (dual of [531456, 531405, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(351, 265728, F3, 2, 7) (dual of [(265728, 2), 531405, 8]-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.