Information on Result #1303041

Linear OA(8166, 32795, F8, 37) (dual of [32795, 32629, 38]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8165, 32793, F8, 37) (dual of [32793, 32628, 38]-code), using
    • construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
      1. linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
      2. linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      3. linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
  2. linear OA(8165, 32794, F8, 36) (dual of [32794, 32629, 37]-code), using Gilbert–VarÅ¡amov bound and bm = 8165 > Vbs−1(k−1) = 4061 838059 799988 339067 713943 399822 023728 479878 669542 849993 209157 480319 613172 275294 669877 887824 353486 853253 596991 962957 231732 850158 110912 541079 044096 [i]
  3. linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-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(8166, 32795, F8, 2, 37) (dual of [(32795, 2), 65424, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8166, 32795, F8, 3, 37) (dual of [(32795, 3), 98219, 38]-NRT-code) [i]
3Digital (129, 166, 32795)-net over F8 [i]