MinT - Information on Result #1195646

Information on Result #1195646

Digital (74, 99, 10923)-net over F₁₆, using net defined by OOA based on linear OOA(16⁹⁹, 10923, F₁₆, 25, 25) (dual of [(10923, 25), 272976, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(16⁹⁹, 131077, F₁₆, 25) (dual of [131077, 130978, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁹⁸, 131076, F₁₆, 25) (dual of [131076, 130978, 26]-code), using
  - trace code [i] based on linear OA(256⁴⁹, 65538, F₂₅₆, 25) (dual of [65538, 65489, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(23) [i] based on
      1. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
      3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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 (75, 100, 10923)-net over F₁₆	[i]	Net Duplication
2	Digital (76, 101, 10923)-net over F₁₆	[i]
3	Digital (77, 102, 10923)-net over F₁₆	[i]