MinT - Information on Result #1192712

Information on Result #1192712

Digital (113, 139, 20167)-net over F₈, using net defined by OOA based on linear OOA(8¹³⁹, 20167, F₈, 26, 26) (dual of [(20167, 26), 524203, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(8¹³⁹, 262171, F₈, 26) (dual of [262171, 262032, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹³⁹, 262174, F₈, 26) (dual of [262174, 262035, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(20) [i] based on
    1. linear OA(8¹³³, 262144, F₈, 26) (dual of [262144, 262011, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(8¹⁰⁹, 262144, F₈, 21) (dual of [262144, 262035, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(8⁶, 30, F₈, 4) (dual of [30, 24, 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 (114, 140, 20167)-net over F₈	[i]	Net Duplication
2	Digital (115, 141, 20167)-net over F₈	[i]
3	Digital (116, 142, 20167)-net over F₈	[i]