Information on Result #1794677
Digital (112, 133, 2097188)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8133, 2097188, F8, 21) (dual of [2097188, 2097055, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8131, 2097185, F8, 21) (dual of [2097185, 2097054, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(8127, 2097153, F8, 21) (dual of [2097153, 2097026, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(8131, 2097186, F8, 19) (dual of [2097186, 2097055, 20]-code), using Gilbert–Varšamov bound and bm = 8131 > Vbs−1(k−1) = 156622 415883 295212 979985 346426 096320 078843 835802 306984 247222 152339 037234 828478 512133 581540 768823 386907 724914 306664 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(8131, 2097185, F8, 21) (dual of [2097185, 2097054, 22]-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.