MinT - Information on Result #1185930

Information on Result #1185930

Digital (53, 61, 262146)-net over F₄, using net defined by OOA based on linear OOA(4⁶¹, 262146, F₄, 8, 8) (dual of [(262146, 8), 2097107, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(4⁶¹, 1048584, F₄, 8) (dual of [1048584, 1048523, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁶¹, 1048587, F₄, 8) (dual of [1048587, 1048526, 9]-code), using
  - 1 times truncation [i] based on linear OA(4⁶², 1048588, F₄, 9) (dual of [1048588, 1048526, 10]-code), using
    - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(4⁶¹, 1048576, F₄, 9) (dual of [1048576, 1048515, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(4⁵¹, 1048576, F₄, 7) (dual of [1048576, 1048525, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(4¹¹, 12, F₄, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
        dual of repetition code with length 12 [i]
      4. linear OA(4¹, 12, F₄, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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 (229, 245, 4456446)-net over F₄	[i]		(u,Â u+v)-Construction for Nets
2	Digital (240, 257, 4456446)-net over F₄	[i]		(u,Â u+v)-Construction for Nets