MinT - Information on Result #1840441

Information on Result #1840441

(73, 89, 262148)-net in base 16, using net defined by OOA based on OOA(16⁸⁹, 262148, S₁₆, 18, 16), using

OOA 4-folding and stacking with additional row [i] based on OOA(16⁸⁹, 1048593, S₁₆, 2, 16), using
- discarding factors based on OOA(16⁸⁹, 1048594, S₁₆, 2, 16), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(16⁸, 17, F₁₆, 2, 8) (dual of [(17, 2), 26, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;26,16) [i]
    2. OOA(16⁸¹, 1048577, S₁₆, 2, 16), using
      - OOA 2-folding [i] based on OA(16⁸¹, 2097154, S₁₆, 16), using
        discarding factors based on OA(16⁸¹, 2097155, S₁₆, 16), using
        discarding parts of the base [i] based on linear OA(128⁴⁶, 2097155, F₁₂₈, 16) (dual of [2097155, 2097109, 17]-code), using
        constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
        linear OA(128⁴⁶, 2097152, F₁₂₈, 16) (dual of [2097152, 2097106, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(128⁴³, 2097152, F₁₂₈, 15) (dual of [2097152, 2097109, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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: Constructive.

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.