MinT - Information on Result #1178847

Information on Result #1178847

Digital (45, 53, 2051)-net over F₂, using net defined by OOA based on linear OOA(2⁵³, 2051, F₂, 8, 8) (dual of [(2051, 8), 16355, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(2⁵³, 8204, F₂, 8) (dual of [8204, 8151, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁵³, 8206, F₂, 8) (dual of [8206, 8153, 9]-code), using
  - 1 times truncation [i] based on linear OA(2⁵⁴, 8207, F₂, 9) (dual of [8207, 8153, 10]-code), using
    - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(2⁵³, 8192, F₂, 9) (dual of [8192, 8139, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(2⁴⁰, 8192, F₂, 7) (dual of [8192, 8152, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
      4. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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		This result only	Method
1	Digital (221, 237, 1050626)-net over F₂	[i]		(u,Â u+v)-Construction for Nets
2	Digital (221, 238, 1050626)-net over F₂	[i]		(u,Â u+v)-Construction for Nets