MinT - Information on Result #1192978

Information on Result #1192978

Digital (131, 168, 1822)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶⁸, 1822, F₈, 37, 37) (dual of [(1822, 37), 67246, 38]-NRT-code), using

OOA 18-folding and stacking with additional row [i] based on linear OA(8¹⁶⁸, 32797, F₈, 37) (dual of [32797, 32629, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁶⁸, 32800, F₈, 37) (dual of [32800, 32632, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(30) [i] based on
    1. linear OA(8¹⁶¹, 32768, F₈, 37) (dual of [32768, 32607, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(8¹³⁶, 32768, F₈, 31) (dual of [32768, 32632, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(8⁷, 32, F₈, 5) (dual of [32, 25, 6]-code), using
      - discarding factors / shortening the dual code 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 (132, 168, 1822)-net over F₈	[i]	t-Expansion
2	Digital (132, 169, 1822)-net over F₈	[i]	Net Duplication
3	Digital (133, 170, 1822)-net over F₈	[i]
4	Digital (134, 171, 1822)-net over F₈	[i]
5	Digital (135, 172, 1822)-net over F₈	[i]
6	Digital (136, 173, 1822)-net over F₈	[i]
7	Digital (131, 167, 1822)-net over F₈	[i]	m-Reduction