MinT - Information on Result #1192728

Information on Result #1192728

Digital (135, 161, 161322)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶¹, 161322, F₈, 26, 26) (dual of [(161322, 26), 4194211, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(8¹⁶¹, 2097186, F₈, 26) (dual of [2097186, 2097025, 27]-code), using
- constructionÂ X applied to C_e(25) âŠ‚ C_e(20) [i] based on
  1. linear OA(8¹⁵⁵, 2097152, F₈, 26) (dual of [2097152, 2096997, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
  2. linear OA(8¹²⁷, 2097152, F₈, 21) (dual of [2097152, 2097025, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  3. linear OA(8⁶, 34, F₈, 4) (dual of [34, 28, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁶, 56, F₈, 4) (dual of [56, 50, 5]-code), using
      - 1 times truncation [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 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 (136, 162, 161322)-net over F₈	[i]	Net Duplication
2	Digital (137, 163, 161322)-net over F₈	[i]
3	Digital (138, 164, 161322)-net over F₈	[i]
4	Digital (139, 165, 161322)-net over F₈	[i]