MinT - Information on Result #1188060

Information on Result #1188060

Digital (20, 25, 7815)-net over F₅, using net defined by OOA based on linear OOA(5²⁵, 7815, F₅, 5, 5) (dual of [(7815, 5), 39050, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(5²⁵, 15631, F₅, 5) (dual of [15631, 15606, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(5²⁵, 15632, F₅, 5) (dual of [15632, 15607, 6]-code), using
  - 1 times truncation [i] based on linear OA(5²⁶, 15633, F₅, 6) (dual of [15633, 15607, 7]-code), using
    - constructionÂ X4 applied to C_e(5) âŠ‚ C_e(3) [i] based on
      1. linear OA(5²⁵, 15625, F₅, 6) (dual of [15625, 15600, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(5¹⁹, 15625, F₅, 4) (dual of [15625, 15606, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(5⁷, 8, F₅, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,5)), using
        dual of repetition code with length 8 [i]
      4. linear OA(5¹, 8, F₅, 1) (dual of [8, 7, 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 (107, 117, 3363255)-net over F₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (116, 127, 3363255)-net over F₅	[i]		(u,Â u+v)-Construction for Nets