MinT - Information on Result #1185080

Information on Result #1185080

Digital (113, 136, 1790)-net over F₃, using net defined by OOA based on linear OOA(3¹³⁶, 1790, F₃, 23, 23) (dual of [(1790, 23), 41034, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(3¹³⁶, 19691, F₃, 23) (dual of [19691, 19555, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹³⁶, 19692, F₃, 23) (dual of [19692, 19556, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
    1. linear OA(3¹³⁶, 19683, F₃, 23) (dual of [19683, 19547, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 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 (114, 137, 1790)-net over F₃	[i]	Net Duplication
2	Digital (115, 138, 1790)-net over F₃	[i]
3	Digital (116, 139, 1790)-net over F₃	[i]
4	Digital (124, 147, 1794)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (125, 148, 1797)-net over F₃	[i]
6	Digital (126, 149, 1798)-net over F₃	[i]
7	Digital (127, 150, 1800)-net over F₃	[i]