MinT - Information on Result #1708896

Information on Result #1708896

Digital (156, 169, 2097661)-net over F₂, using net defined by OOA based on linear OOA(2¹⁶⁹, 2097661, F₂, 18, 13) (dual of [(2097661, 18), 37757729, 14]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁶⁹, 2097662, F₂, 6, 13) (dual of [(2097662, 6), 12585803, 14]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁶⁹, 2097662, F₂, 4, 13) (dual of [(2097662, 4), 8390479, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2³⁰, 512, F₂, 4, 6) (dual of [(512, 4), 2018, 7]-NRT-code), using
      - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³⁰, 512, F₂, 2, 6) (dual of [(512, 2), 994, 7]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(2²⁸, 511, F₂, 2, 6) (dual of [(511, 2), 994, 7]-NRT-code), using
        OOAs constructed from BCH codes [i]
    2. linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.