MinT - Information on Result #1195554

Information on Result #1195554

Digital (86, 108, 95328)-net over F₁₆, using net defined by OOA based on linear OOA(16¹⁰⁸, 95328, F₁₆, 22, 22) (dual of [(95328, 22), 2097108, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(16¹⁰⁸, 1048608, F₁₆, 22) (dual of [1048608, 1048500, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16¹⁰⁷, 1048607, F₁₆, 22) (dual of [1048607, 1048500, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
    1. linear OA(16¹⁰¹, 1048576, F₁₆, 22) (dual of [1048576, 1048475, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(16⁶, 31, F₁₆, 4) (dual of [31, 25, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(16⁶, 240, F₁₆, 4) (dual of [240, 234, 5]-code), using
        1 times truncation [i] based on linear OA(16⁷, 241, F₁₆, 5) (dual of [241, 234, 6]-code), using
        a code by Danev and Olsson [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 (87, 109, 95328)-net over F₁₆	[i]	Net Duplication
2	Digital (88, 110, 95328)-net over F₁₆	[i]
3	Digital (89, 111, 95328)-net over F₁₆	[i]