Information on Result #1712290
Digital (37, 44, 29531)-net over F3, using net defined by OOA based on linear OOA(344, 29531, F3, 9, 7) (dual of [(29531, 9), 265735, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(344, 29532, F3, 3, 7) (dual of [(29532, 3), 88552, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(344, 29532, F3, 2, 7) (dual of [(29532, 2), 59020, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(344, 59064, F3, 7) (dual of [59064, 59020, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(342, 59061, F3, 7) (dual of [59061, 59019, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(341, 59049, F3, 7) (dual of [59049, 59008, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(331, 59049, F3, 5) (dual of [59049, 59018, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(311, 12, F3, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
- dual of repetition code with length 12 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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
- linear OA(342, 59062, F3, 5) (dual of [59062, 59020, 6]-code), using Gilbert–Varšamov bound and bm = 342 > Vbs−1(k−1) = 8 111151 471710 321043 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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 (see above)
- linear OA(342, 59061, F3, 7) (dual of [59061, 59019, 8]-code), using
- construction X with Varšamov bound [i] based on
- OOA 2-folding [i] based on linear OA(344, 59064, F3, 7) (dual of [59064, 59020, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(344, 29532, F3, 2, 7) (dual of [(29532, 2), 59020, 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.