MinT - Information on Result #3188752

Information on Result #3188752

Digital (198, 218, 209720)-net over F₂, using t-expansion based on digital (197, 218, 209720)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²¹⁸, 209720, F₂, 21, 21) (dual of [(209720, 21), 4403902, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2²¹⁸, 2097201, F₂, 21) (dual of [2097201, 2096983, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹⁸, 2097202, F₂, 21) (dual of [2097202, 2096984, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(2²¹¹, 2097153, F₂, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 2⁴²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(2¹⁶⁹, 2097153, F₂, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 2⁴²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(2⁷, 49, F₂, 3) (dual of [49, 42, 4]-code or 49-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 (199, 219, 209720)-net over F₂	[i]		Net Duplication