MinT - Information on Result #1188076

Information on Result #1188076

Digital (28, 33, 195316)-net over F₅, using net defined by OOA based on linear OOA(5³³, 195316, F₅, 5, 5) (dual of [(195316, 5), 976547, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(5³³, 390633, F₅, 5) (dual of [390633, 390600, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(5³³, 390634, F₅, 5) (dual of [390634, 390601, 6]-code), using
  - 1 times truncation [i] based on linear OA(5³⁴, 390635, F₅, 6) (dual of [390635, 390601, 7]-code), using
    - constructionÂ X4 applied to C_e(5) âŠ‚ C_e(3) [i] based on
      1. linear OA(5³³, 390625, F₅, 6) (dual of [390625, 390592, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(5²⁵, 390625, F₅, 4) (dual of [390625, 390600, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(5⁹, 10, F₅, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,5)), using
        dual of repetition code with length 10 [i]
      4. linear OA(5¹, 10, F₅, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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 (115, 125, 3550756)-net over F₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (124, 135, 3550756)-net over F₅	[i]		(u,Â u+v)-Construction for Nets