MinT - Information on Result #1195142

Information on Result #1195142

Digital (48, 61, 174763)-net over F₁₆, using net defined by OOA based on linear OOA(16⁶¹, 174763, F₁₆, 13, 13) (dual of [(174763, 13), 2271858, 14]-NRT-code), using

OOA 6-folding and stacking with additional row [i] based on linear OA(16⁶¹, 1048579, F₁₆, 13) (dual of [1048579, 1048518, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁶¹, 1048581, F₁₆, 13) (dual of [1048581, 1048520, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(16⁶¹, 1048576, F₁₆, 13) (dual of [1048576, 1048515, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(16⁵⁶, 1048576, F₁₆, 12) (dual of [1048576, 1048520, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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 (54, 67, 174780)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets
2	Digital (55, 68, 174787)-net over F₁₆	[i]
3	Digital (56, 69, 174796)-net over F₁₆	[i]
4	Digital (57, 70, 174801)-net over F₁₆	[i]
5	Digital (58, 71, 174808)-net over F₁₆	[i]
6	Digital (59, 72, 175020)-net over F₁₆	[i]