MinT - Information on Result #1750211

Information on Result #1750211

Digital (93, 103, 311442)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰³, 311442, F₂, 3, 10) (dual of [(311442, 3), 934223, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁰³, 349533, F₂, 3, 10) (dual of [(349533, 3), 1048496, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹⁰³, 1048599, F₂, 10) (dual of [1048599, 1048496, 11]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹⁰¹, 1048597, F₂, 10) (dual of [1048597, 1048496, 11]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁰², 1048598, F₂, 11) (dual of [1048598, 1048496, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2¹⁰¹, 1048576, F₂, 11) (dual of [1048576, 1048475, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2⁸¹, 1048576, F₂, 9) (dual of [1048576, 1048495, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2²¹, 22, F₂, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
        dual of repetition code with length 22 [i]
        linear OA(2¹, 22, F₂, 1) (dual of [22, 21, 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.