MinT - Information on Result #1840401

Information on Result #1840401

(58, 71, 349531)-net in base 16, using net defined by OOA based on OOA(16⁷¹, 349531, S₁₆, 14, 13), using

OOA 3-folding and stacking with additional row [i] based on OOA(16⁷¹, 1048594, S₁₆, 2, 13), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(16⁶, 17, F₁₆, 2, 6) (dual of [(17, 2), 28, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;28,16) [i]
  2. OOA(16⁶⁵, 1048577, S₁₆, 2, 13), using
    - OOA 2-folding [i] based on OA(16⁶⁵, 2097154, S₁₆, 13), using
      - discarding factors based on OA(16⁶⁵, 2097155, S₁₆, 13), using
        discarding parts of the base [i] based on linear OA(128³⁷, 2097155, F₁₂₈, 13) (dual of [2097155, 2097118, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(128³⁷, 2097152, F₁₂₈, 13) (dual of [2097152, 2097115, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.