MinT - Information on Result #1187778

Information on Result #1187778

Digital (164, 195, 4372)-net over F₄, using net defined by OOA based on linear OOA(4¹⁹⁵, 4372, F₄, 31, 31) (dual of [(4372, 31), 135337, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(4¹⁹⁵, 65581, F₄, 31) (dual of [65581, 65386, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁹⁵, 65586, F₄, 31) (dual of [65586, 65391, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
    1. linear OA(4¹⁸⁵, 65536, F₄, 31) (dual of [65536, 65351, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(4¹⁴⁵, 65536, F₄, 25) (dual of [65536, 65391, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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 (165, 196, 4372)-net over F₄	[i]	Net Duplication
2	Digital (166, 197, 4372)-net over F₄	[i]
3	Digital (167, 198, 4372)-net over F₄	[i]
4	Digital (168, 199, 4372)-net over F₄	[i]