MinT - Information on Result #1205061

Information on Result #1205061

Digital (106, 116, 1913190)-net over F₃, using trace code for nets based on digital (48, 58, 956595)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁵⁸, 956595, F₉, 10, 10) (dual of [(956595, 10), 9565892, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(9⁵⁸, 4782975, F₉, 10) (dual of [4782975, 4782917, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁵⁸, 4782977, F₉, 10) (dual of [4782977, 4782919, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(9⁵⁰, 4782969, F₉, 8) (dual of [4782969, 4782919, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(9¹, 8, F₉, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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 (107, 117, 1913190)-net over F₃	[i]		Net Duplication
2	Digital (108, 118, 1913190)-net over F₃	[i]
3	Digital (109, 119, 1913190)-net over F₃	[i]
4	Linear OOA(3¹¹⁶, 1913190, F₃, 5, 10) (dual of [(1913190, 5), 9565834, 11]-NRT-code)	[i]		Extracting Embedded OOA