MinT - Information on Result #1179336

Information on Result #1179336

Digital (27, 33, 2190)-net over F₃, using net defined by OOA based on linear OOA(3³³, 2190, F₃, 6, 6) (dual of [(2190, 6), 13107, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3³³, 2190, F₃, 5, 6) (dual of [(2190, 5), 10917, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3³³, 6570, F₃, 6) (dual of [6570, 6537, 7]-code), using
  - 1 times truncation [i] based on linear OA(3³⁴, 6571, F₃, 7) (dual of [6571, 6537, 8]-code), using
    - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
      1. linear OA(3³³, 6561, F₃, 7) (dual of [6561, 6528, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3²⁵, 6561, F₃, 5) (dual of [6561, 6536, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(3⁹, 10, F₃, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
        dual of repetition code with length 10 [i]
      4. linear OA(3¹, 10, F₃, 1) (dual of [10, 9, 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		This result only	Method
1	Digital (201, 213, 5594590)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (141, 154, 1400290)-net over F₃	[i]
3	Digital (216, 229, 5594590)-net over F₃	[i]