MinT - Information on Result #1179380

Information on Result #1179380

Digital (52, 58, 1594333)-net over F₃, using net defined by OOA based on linear OOA(3⁵⁸, 1594333, F₃, 6, 6) (dual of [(1594333, 6), 9565940, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3⁵⁸, 1594333, F₃, 5, 6) (dual of [(1594333, 5), 7971607, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3⁵⁸, 4782999, F₃, 6) (dual of [4782999, 4782941, 7]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(3) [i] based on
    1. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3²⁹, 4782969, F₃, 4) (dual of [4782969, 4782940, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(3²⁹, 30, F₃, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
      - dual of repetition code with length 30 [i]
    4. linear OA(3¹, 30, F₃, 1) (dual of [30, 29, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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 (53, 59, 1594333)-net over F₃	[i]	Net Duplication
2	Digital (214, 226, 5788633)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
3	Digital (226, 238, 7186733)-net over F₃	[i]
4	Digital (228, 241, 5788633)-net over F₃	[i]