MinT - Information on Result #3191820

Information on Result #3191820

Digital (218, 246, 9365)-net over F₂, using t-expansion based on digital (217, 246, 9365)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁴⁶, 9365, F₂, 29, 29) (dual of [(9365, 29), 271339, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2²⁴⁶, 131111, F₂, 29) (dual of [131111, 130865, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁴⁶, 131114, F₂, 29) (dual of [131114, 130868, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(2²³⁹, 131073, F₂, 29) (dual of [131073, 130834, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. linear OA(2²⁰⁵, 131073, F₂, 25) (dual of [131073, 130868, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(2⁷, 41, F₂, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 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 (219, 247, 9365)-net over F₂	[i]		Net Duplication
2	Digital (220, 248, 9365)-net over F₂	[i]
3	Digital (221, 249, 9365)-net over F₂	[i]
4	Digital (222, 250, 9365)-net over F₂	[i]