MinT - Information on Result #1187152

Information on Result #1187152

Digital (123, 145, 23832)-net over F₄, using net defined by OOA based on linear OOA(4¹⁴⁵, 23832, F₄, 22, 22) (dual of [(23832, 22), 524159, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(4¹⁴⁵, 262152, F₄, 22) (dual of [262152, 262007, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, 262153, F₄, 22) (dual of [262153, 262008, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
    1. linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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 (124, 146, 23832)-net over F₄	[i]	Net Duplication
2	Digital (125, 147, 23832)-net over F₄	[i]	Net Duplication
3	Digital (134, 156, 23837)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
4	Digital (135, 157, 23841)-net over F₄	[i]
5	Digital (136, 158, 23842)-net over F₄	[i]
6	Digital (137, 159, 23846)-net over F₄	[i]
7	Digital (138, 160, 23847)-net over F₄	[i]