MinT - Information on Result #1755785

Information on Result #1755785

Digital (178, 207, 3413)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁷, 3413, F₂, 4, 29) (dual of [(3413, 4), 13445, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁷, 4105, F₂, 4, 29) (dual of [(4105, 4), 16213, 30]-NRT-code), using
- 2³ times duplication [i] based on linear OOA(2²⁰⁴, 4105, F₂, 4, 29) (dual of [(4105, 4), 16216, 30]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2²⁰⁴, 16420, F₂, 29) (dual of [16420, 16216, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(2¹⁹⁷, 16385, F₂, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. linear OA(2¹⁶⁹, 16385, F₂, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-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.