MinT - Information on Result #1757746

Information on Result #1757746

Digital (203, 232, 10929)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³², 10929, F₂, 6, 29) (dual of [(10929, 6), 65342, 30]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²³², 65574, F₂, 29) (dual of [65574, 65342, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2²³², 65576, F₂, 29) (dual of [65576, 65344, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2²²⁵, 65537, F₂, 29) (dual of [65537, 65312, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹⁹³, 65537, F₂, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’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, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-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: 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 (204, 233, 10929)-net over F₂	[i]		Net Duplication
2	Digital (205, 234, 10929)-net over F₂	[i]
3	Digital (206, 235, 10929)-net over F₂	[i]