MinT - Information on Result #1849472

Information on Result #1849472

(26, 37, 524288)-net in base 64, using net defined by OOA based on OOA(64³⁷, 524288, S₆₄, 15, 11), using

OOA 2-folding and stacking with additional row [i] based on OOA(64³⁷, 1048577, S₆₄, 3, 11), using
- discarding parts of the base [i] based on linear OOA(128³¹, 1048577, F₁₂₈, 3, 11) (dual of [(1048577, 3), 3145700, 12]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(128³¹, 1048577, F₁₂₈, 2, 11) (dual of [(1048577, 2), 2097123, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128³¹, 2097154, F₁₂₈, 11) (dual of [2097154, 2097123, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(128³¹, 2097155, F₁₂₈, 11) (dual of [2097155, 2097124, 12]-code), using
        constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Arbitrary.

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.