MinT - Information on Result #1771630

Information on Result #1771630

Digital (216, 242, 1108738)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴², 1108738, F₃, 4, 26) (dual of [(1108738, 4), 4434710, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴², 1195746, F₃, 4, 26) (dual of [(1195746, 4), 4782742, 27]-NRT-code), using
- 3² times duplication [i] based on linear OOA(3²⁴⁰, 1195746, F₃, 4, 26) (dual of [(1195746, 4), 4782744, 27]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²⁴⁰, 4782984, F₃, 26) (dual of [4782984, 4782744, 27]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3²³⁹, 4782983, F₃, 26) (dual of [4782983, 4782744, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        linear OA(3²³⁹, 4782969, F₃, 26) (dual of [4782969, 4782730, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(3²²⁵, 4782969, F₃, 25) (dual of [4782969, 4782744, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 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.