Information on Result #1768558
Digital (189, 208, 4194396)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3208, 4194396, F3, 2, 19) (dual of [(4194396, 2), 8388584, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(327, 95, F3, 2, 9) (dual of [(95, 2), 163, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(327, 95, F3, 9) (dual of [95, 68, 10]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(326, 92, F3, 9) (dual of [92, 66, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(325, 82, F3, 9) (dual of [82, 57, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(317, 82, F3, 7) (dual of [82, 65, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(39, 10, F3, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
- dual of repetition code with length 10 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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 C([0,4]) ⊂ C([0,3]) [i] based on
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(326, 92, F3, 9) (dual of [92, 66, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(327, 95, F3, 9) (dual of [95, 68, 10]-code), using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- linear OOA(327, 95, F3, 2, 9) (dual of [(95, 2), 163, 10]-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.