MinT - Information on Result #1712874

Information on Result #1712874

Digital (67, 78, 64159)-net over F₃, using net defined by OOA based on linear OOA(3⁷⁸, 64159, F₃, 15, 11) (dual of [(64159, 15), 962307, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3⁷⁸, 64160, F₃, 5, 11) (dual of [(64160, 5), 320722, 12]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷⁸, 64160, F₃, 2, 11) (dual of [(64160, 2), 128242, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁷⁸, 88579, F₃, 2, 11) (dual of [(88579, 2), 177080, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3⁷⁸, 177158, F₃, 11) (dual of [177158, 177080, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(3⁷⁸, 177147, F₃, 11) (dual of [177147, 177069, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

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.