MinT - Information on Result #1185332

Information on Result #1185332

Digital (196, 222, 122641)-net over F₃, using net defined by OOA based on linear OOA(3²²², 122641, F₃, 26, 26) (dual of [(122641, 26), 3188444, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(3²²², 1594333, F₃, 26) (dual of [1594333, 1594111, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3²²², 1594336, F₃, 26) (dual of [1594336, 1594114, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(3²²², 1594323, F₃, 26) (dual of [1594323, 1594101, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3²⁰⁹, 1594323, F₃, 25) (dual of [1594323, 1594114, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(3⁰, 13, F₃, 0) (dual of [13, 13, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (197, 223, 122641)-net over F₃	[i]	Net Duplication
2	Digital (198, 224, 122641)-net over F₃	[i]
3	Digital (199, 225, 122641)-net over F₃	[i]
4	Digital (210, 236, 122648)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (211, 237, 122649)-net over F₃	[i]
6	Digital (212, 238, 122651)-net over F₃	[i]