MinT - Information on Result #1204178

Information on Result #1204178

Digital (36, 65, 1172)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁵, 1172, F₁₂₈, 29, 29) (dual of [(1172, 29), 33923, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(128⁶⁵, 16409, F₁₂₈, 29) (dual of [16409, 16344, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁶⁵, 16410, F₁₂₈, 29) (dual of [16410, 16345, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(19) [i] based on
    1. linear OA(128⁵⁷, 16384, F₁₂₈, 29) (dual of [16384, 16327, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(128³⁹, 16384, F₁₂₈, 20) (dual of [16384, 16345, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(128⁸, 26, F₁₂₈, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁸, 128, F₁₂₈, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
        Reedâ€“Solomon code RS(120,128) [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 (37, 65, 1172)-net over F₁₂₈	[i]	t-Expansion
2	Digital (37, 66, 1172)-net over F₁₂₈	[i]	Net Duplication
3	Digital (38, 67, 1172)-net over F₁₂₈	[i]
4	Digital (39, 68, 1172)-net over F₁₂₈	[i]
5	Digital (40, 69, 1172)-net over F₁₂₈	[i]
6	Digital (36, 64, 1172)-net over F₁₂₈	[i]	m-Reduction