MinT - Information on Result #1188022

Information on Result #1188022

Digital (205, 246, 3278)-net over F₄, using net defined by OOA based on linear OOA(4²⁴⁶, 3278, F₄, 41, 41) (dual of [(3278, 41), 134152, 42]-NRT-code), using

OOA 20-folding and stacking with additional row [i] based on linear OA(4²⁴⁶, 65561, F₄, 41) (dual of [65561, 65315, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4²⁴⁶, 65565, F₄, 41) (dual of [65565, 65319, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(36) [i] based on
    1. linear OA(4²⁴¹, 65536, F₄, 41) (dual of [65536, 65295, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(4²¹⁷, 65536, F₄, 37) (dual of [65536, 65319, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    3. linear OA(4⁵, 29, F₄, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
      - discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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 (206, 246, 3278)-net over F₄	[i]	t-Expansion
2	Digital (206, 247, 3278)-net over F₄	[i]	Net Duplication
3	Digital (207, 248, 3278)-net over F₄	[i]
4	Digital (208, 249, 3278)-net over F₄	[i]
5	Digital (209, 250, 3278)-net over F₄	[i]
6	Digital (210, 251, 3278)-net over F₄	[i]
7	Digital (211, 252, 3278)-net over F₄	[i]