MinT - Information on Result #1749489

Information on Result #1749489

Digital (64, 75, 4210)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁷⁵, 4210, F₂, 3, 11) (dual of [(4210, 3), 12555, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁷⁵, 5467, F₂, 3, 11) (dual of [(5467, 3), 16326, 12]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2⁷³, 5467, F₂, 3, 11) (dual of [(5467, 3), 16328, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁷³, 16401, F₂, 11) (dual of [16401, 16328, 12]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2⁷², 16400, F₂, 11) (dual of [16400, 16328, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2⁷¹, 16384, F₂, 11) (dual of [16384, 16313, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2⁵⁷, 16384, F₂, 9) (dual of [16384, 16327, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2¹⁵, 16, F₂, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
        dual of repetition code with length 16 [i]
        linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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.