MinT - Information on Result #1179330

Information on Result #1179330

Digital (23, 29, 731)-net over F₃, using net defined by OOA based on linear OOA(3²⁹, 731, F₃, 6, 6) (dual of [(731, 6), 4357, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3²⁹, 731, F₃, 5, 6) (dual of [(731, 5), 3626, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3²⁹, 2193, F₃, 6) (dual of [2193, 2164, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁹, 2195, F₃, 6) (dual of [2195, 2166, 7]-code), using
    - 1 times truncation [i] based on linear OA(3³⁰, 2196, F₃, 7) (dual of [2196, 2166, 8]-code), using
      - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
        linear OA(3²⁹, 2187, F₃, 7) (dual of [2187, 2158, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(3²², 2187, F₃, 5) (dual of [2187, 2165, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(3⁸, 9, F₃, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
        dual of repetition code with length 9 [i]
        linear OA(3¹, 9, F₃, 1) (dual of [9, 8, 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 (197, 209, 5593131)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (137, 150, 1398831)-net over F₃	[i]
3	Digital (212, 225, 5593131)-net over F₃	[i]