MinT - Information on Result #1762016

Information on Result #1762016

Digital (91, 102, 1732503)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰², 1732503, F₃, 2, 11) (dual of [(1732503, 2), 3464904, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰², 2391493, F₃, 2, 11) (dual of [(2391493, 2), 4782884, 12]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁰¹, 2391493, F₃, 2, 11) (dual of [(2391493, 2), 4782885, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰¹, 4782986, F₃, 11) (dual of [4782986, 4782885, 12]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁰, 4782985, F₃, 11) (dual of [4782985, 4782885, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(3⁹⁹, 4782969, F₃, 11) (dual of [4782969, 4782870, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(3⁸⁵, 4782969, F₃, 10) (dual of [4782969, 4782884, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(3¹⁵, 16, F₃, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
        dual of repetition code with length 16 [i]
        linear OA(3¹, 16, F₃, 1) (dual of [16, 15, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.