MinT - Information on Result #3213576

Information on Result #3213576

Digital (164, 196, 4097)-net over F₄, using t-expansion based on digital (163, 196, 4097)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁹⁶, 4097, F₄, 33, 33) (dual of [(4097, 33), 135005, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4¹⁹⁶, 65553, F₄, 33) (dual of [65553, 65357, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹⁶, 65555, F₄, 33) (dual of [65555, 65359, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(29) [i] based on
      1. linear OA(4¹⁹³, 65536, F₄, 33) (dual of [65536, 65343, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4¹⁷⁷, 65536, F₄, 30) (dual of [65536, 65359, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      3. linear OA(4³, 19, F₄, 2) (dual of [19, 16, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [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 (165, 197, 4097)-net over F₄	[i]		Net Duplication
2	Digital (166, 198, 4097)-net over F₄	[i]
3	Digital (167, 199, 4097)-net over F₄	[i]