MinT - Information on Result #1186734

Information on Result #1186734

Digital (100, 118, 29128)-net over F₄, using net defined by OOA based on linear OOA(4¹¹⁸, 29128, F₄, 18, 18) (dual of [(29128, 18), 524186, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(4¹¹⁸, 262152, F₄, 18) (dual of [262152, 262034, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹¹⁸, 262153, F₄, 18) (dual of [262153, 262035, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(4¹¹⁸, 262144, F₄, 18) (dual of [262144, 262026, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(4¹⁰⁹, 262144, F₄, 17) (dual of [262144, 262035, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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 and 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

The following results depend on this result:

	Result		Method
1	Digital (101, 119, 29128)-net over F₄	[i]	Net Duplication
2	Digital (102, 120, 29128)-net over F₄	[i]	Net Duplication
3	Digital (109, 127, 29133)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
4	Digital (110, 128, 29137)-net over F₄	[i]
5	Digital (111, 129, 29138)-net over F₄	[i]
6	Digital (112, 130, 29142)-net over F₄	[i]