MinT - Information on Result #1778016

Information on Result #1778016

Digital (153, 174, 1425681)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁷⁴, 1425681, F₄, 2, 21) (dual of [(1425681, 2), 2851188, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁷⁴, 2097172, F₄, 2, 21) (dual of [(2097172, 2), 4194170, 22]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁷³, 2097172, F₄, 2, 21) (dual of [(2097172, 2), 4194171, 22]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁷¹, 2097171, F₄, 2, 21) (dual of [(2097171, 2), 4194171, 22]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(4¹⁷¹, 4194342, F₄, 21) (dual of [4194342, 4194171, 22]-code), using
      - constructionÂ X applied to C_e(20) âŠ‚ C_e(16) [i] based on
        linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4¹³³, 4194304, F₄, 17) (dual of [4194304, 4194171, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(4⁵, 38, F₄, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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.