MinT - Information on Result #1798223

Information on Result #1798223

Digital (70, 83, 4782997)-net over F₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(9⁸³, 4782997, F₉, 13) (dual of [4782997, 4782914, 14]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(9⁸¹, 4782993, F₉, 13) (dual of [4782993, 4782912, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(9) [i] based on
    1. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(9³, 24, F₉, 2) (dual of [24, 21, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(9³, 80, F₉, 2) (dual of [80, 77, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 9²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
2. linear OA(9⁸¹, 4782995, F₉, 12) (dual of [4782995, 4782914, 13]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9⁸¹Â > V_b^sâˆ’1(kâˆ’1)Â = 6449 521079 776401 215371 956098 495556 207324 773567 379523 843934 556889 342143 427281 [i]
3. linear OA(9⁰, 2, F₉, 0) (dual of [2, 2, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.