Information on Result #1715274
Digital (165, 189, 25637)-net over F3, using net defined by OOA based on linear OOA(3189, 25637, F3, 28, 24) (dual of [(25637, 28), 717647, 25]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3189, 76912, F3, 4, 24) (dual of [(76912, 4), 307459, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3189, 76913, F3, 4, 24) (dual of [(76913, 4), 307463, 25]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3189, 76913, F3, 2, 24) (dual of [(76913, 2), 153637, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3189, 88602, F3, 2, 24) (dual of [(88602, 2), 177015, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(3189, 88602, F3, 2, 25) (dual of [(88602, 2), 177015, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3189, 177204, F3, 25) (dual of [177204, 177015, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3177, 177148, F3, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(312, 56, F3, 5) (dual of [56, 44, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- (u, u+v)-construction [i] based on
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- OOA 2-folding [i] based on linear OA(3189, 177204, F3, 25) (dual of [177204, 177015, 26]-code), using
- strength reduction [i] based on linear OOA(3189, 88602, F3, 2, 25) (dual of [(88602, 2), 177015, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3189, 88602, F3, 2, 24) (dual of [(88602, 2), 177015, 25]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3189, 76913, F3, 2, 24) (dual of [(76913, 2), 153637, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3189, 76913, F3, 4, 24) (dual of [(76913, 4), 307463, 25]-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.