MinT - Information on Result #1179634

Information on Result #1179634

Digital (3, 7, 1201)-net over F₄₉, using net defined by OOA based on linear OOA(49⁷, 1201, F₄₉, 4, 4) (dual of [(1201, 4), 4797, 5]-NRT-code), using

appending kth column [i] based on linear OOA(49⁷, 1201, F₄₉, 3, 4) (dual of [(1201, 3), 3596, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(49⁷, 2402, F₄₉, 4) (dual of [2402, 2395, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁷, 2403, F₄₉, 4) (dual of [2403, 2396, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(49⁷, 2401, F₄₉, 4) (dual of [2401, 2394, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(49⁵, 2401, F₄₉, 3) (dual of [2401, 2396, 4]-code or 2401-cap in PG(4,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (46, 54, 4195502)-net over F₄₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (23, 32, 30613)-net over F₄₉	[i]
3	Digital (31, 40, 1442402)-net over F₄₉	[i]