MinT - Information on Result #1753271

Information on Result #1753271

Digital (149, 170, 13115)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁰, 13115, F₂, 5, 21) (dual of [(13115, 5), 65405, 22]-NRT-code), using

2² times duplication [i] based on linear OOA(2¹⁶⁸, 13115, F₂, 5, 21) (dual of [(13115, 5), 65407, 22]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹⁶⁸, 65575, F₂, 21) (dual of [65575, 65407, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶⁸, 65576, F₂, 21) (dual of [65576, 65408, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(2¹⁶¹, 65537, F₂, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(2¹²⁹, 65537, F₂, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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.