Information on Result #1302858

Linear OA(8133, 2097188, F8, 21) (dual of [2097188, 2097055, 22]-code), using construction X with VarÅ¡amov bound based on
  1. 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
      1. 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]
      2. 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]
      3. linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
  2. linear OA(8131, 2097186, F8, 19) (dual of [2097186, 2097055, 20]-code), using Gilbert–VarÅ¡amov 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]
  3. linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(8133, 2097188, F8, 2, 21) (dual of [(2097188, 2), 4194243, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8133, 2097188, F8, 3, 21) (dual of [(2097188, 3), 6291431, 22]-NRT-code) [i]
3Digital (112, 133, 2097188)-net over F8 [i]
4Linear OOA(8133, 1048594, F8, 2, 21) (dual of [(1048594, 2), 2097055, 22]-NRT-code) [i]OOA Folding