MinT - Information on Result #1797266

Information on Result #1797266

Digital (146, 173, 2097206)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8¹⁷³, 2097206, F₈, 27) (dual of [2097206, 2097033, 28]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8¹⁷², 2097204, F₈, 27) (dual of [2097204, 2097032, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(19) [i] based on
    1. linear OA(8¹⁶², 2097152, F₈, 27) (dual of [2097152, 2096990, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(8¹²⁰, 2097152, F₈, 20) (dual of [2097152, 2097032, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(8¹⁰, 52, F₈, 6) (dual of [52, 42, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹⁰, 74, F₈, 6) (dual of [74, 64, 7]-code), using
        a â€œGraXâ€ code from Grasslâ€™s database [i]
2. linear OA(8¹⁷², 2097205, F₈, 26) (dual of [2097205, 2097033, 27]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8¹⁷²Â > V_b^sâˆ’1(kâˆ’1)Â = 9500 815193 014620 997069 268746 727933 157413 684673 545155 958853 272828 168507 691871 221601 046024 092865 757511 128287 613836 009924 065728 266684 400524 396964 434189 400892 [i]
3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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.