MinT - Information on Result #1180946

Information on Result #1180946

Digital (114, 129, 37452)-net over F₂, using net defined by OOA based on linear OOA(2¹²⁹, 37452, F₂, 15, 15) (dual of [(37452, 15), 561651, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(2¹²⁹, 262165, F₂, 15) (dual of [262165, 262036, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2¹²⁸, 262164, F₂, 15) (dual of [262164, 262036, 16]-code), using
  - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
    1. linear OA(2¹²⁷, 262144, F₂, 15) (dual of [262144, 262017, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(2¹⁰⁹, 262144, F₂, 13) (dual of [262144, 262035, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
      - dual of repetition code with length 20 [i]
    4. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (115, 129, 37452)-net over F₂	[i]	t-Expansion
2	Digital (115, 130, 37452)-net over F₂	[i]	Net Duplication
3	Digital (116, 131, 37452)-net over F₂	[i]
4	Digital (117, 132, 37452)-net over F₂	[i]