MinT - Information on Result #1749687

Information on Result #1749687

Digital (71, 84, 2111)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁸⁴, 2111, F₂, 3, 13) (dual of [(2111, 3), 6249, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁸⁴, 2737, F₂, 3, 13) (dual of [(2737, 3), 8127, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁸¹, 2736, F₂, 3, 13) (dual of [(2736, 3), 8127, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁸¹, 8208, F₂, 13) (dual of [8208, 8127, 14]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2⁸⁰, 8207, F₂, 13) (dual of [8207, 8127, 14]-code), using
      - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
        linear OA(2⁷⁹, 8192, F₂, 13) (dual of [8192, 8113, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2⁶⁶, 8192, F₂, 11) (dual of [8192, 8126, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
        linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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.