MinT - Information on Result #1192948

Information on Result #1192948

Digital (124, 158, 1930)-net over F₈, using net defined by OOA based on linear OOA(8¹⁵⁸, 1930, F₈, 34, 34) (dual of [(1930, 34), 65462, 35]-NRT-code), using

OA 17-folding and stacking [i] based on linear OA(8¹⁵⁸, 32810, F₈, 34) (dual of [32810, 32652, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8¹⁵⁷, 32809, F₈, 34) (dual of [32809, 32652, 35]-code), using
  - constructionÂ X applied to C_e(33) âŠ‚ C_e(26) [i] based on
    1. linear OA(8¹⁴⁶, 32768, F₈, 34) (dual of [32768, 32622, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
    2. linear OA(8¹¹⁶, 32768, F₈, 27) (dual of [32768, 32652, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    3. linear OA(8¹¹, 41, F₈, 6) (dual of [41, 30, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹¹, 63, F₈, 6) (dual of [63, 52, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 8²âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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 (125, 159, 1930)-net over F₈	[i]	Net Duplication
2	Digital (126, 160, 1930)-net over F₈	[i]
3	Digital (127, 161, 1930)-net over F₈	[i]