MinT - Information on Result #3253715

Information on Result #3253715

Digital (157, 170, 1594367)-net over F₃, using 3¹ times duplication based on digital (156, 169, 1594367)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 13, 42)-net over F₃, using
  - linear code embedding found in a computer search [i]
2. digital (143, 156, 1594325)-net over F₃, using
  - net defined by OOA [i] based on linear OOA(3¹⁵⁶, 1594325, F₃, 14, 13) (dual of [(1594325, 14), 22320394, 14]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OOA(3¹⁵⁶, 4782976, F₃, 2, 13) (dual of [(4782976, 2), 9565796, 14]-NRT-code), using
      - trace code [i] based on linear OOA(9⁷⁸, 2391488, F₉, 2, 13) (dual of [(2391488, 2), 4782898, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(9⁷⁸, 4782976, F₉, 13) (dual of [4782976, 4782898, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        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]
        linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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: Constructive and 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.