MinT - Information on Result #1187998

Information on Result #1187998

Digital (195, 234, 3450)-net over F₄, using net defined by OOA based on linear OOA(4²³⁴, 3450, F₄, 39, 39) (dual of [(3450, 39), 134316, 40]-NRT-code), using

OOA 19-folding and stacking with additional row [i] based on linear OA(4²³⁴, 65551, F₄, 39) (dual of [65551, 65317, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(4²³⁴, 65553, F₄, 39) (dual of [65553, 65319, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(36) [i] based on
    1. linear OA(4²³³, 65536, F₄, 39) (dual of [65536, 65303, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [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(4¹, 17, F₄, 1) (dual of [17, 16, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (196, 235, 3450)-net over F₄	[i]	Net Duplication
2	Digital (197, 236, 3450)-net over F₄	[i]
3	Digital (198, 237, 3450)-net over F₄	[i]
4	Digital (199, 238, 3450)-net over F₄	[i]
5	Digital (200, 239, 3450)-net over F₄	[i]
6	Digital (219, 258, 3467)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
7	Digital (221, 260, 3471)-net over F₄	[i]	(u,Â u+v)-Construction for Nets