Information on Result #1299840

Linear OA(457, 262166, F4, 8) (dual of [262166, 262109, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(456, 262164, F4, 8) (dual of [262164, 262108, 9]-code), using
    • construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
      1. linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
      4. linear OA(41, 20, F4, 1) (dual of [20, 19, 2]-code), using
  2. linear OA(456, 262165, F4, 7) (dual of [262165, 262109, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 456 > Vbs−1(k−1) = 328 709173 709519 950796 736532 717564 [i]
  3. linear OA(40, 1, F4, 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(457, 262166, F4, 2, 8) (dual of [(262166, 2), 524275, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(457, 262166, F4, 3, 8) (dual of [(262166, 3), 786441, 9]-NRT-code) [i]
3Digital (49, 57, 262166)-net over F4 [i]
4Linear OOA(457, 131083, F4, 2, 8) (dual of [(131083, 2), 262109, 9]-NRT-code) [i]OOA Folding