MinT - Information on Result #1755206

Information on Result #1755206

Digital (175, 199, 13115)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁹, 13115, F₂, 5, 24) (dual of [(13115, 5), 65376, 25]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁹⁹, 65575, F₂, 24) (dual of [65575, 65376, 25]-code), using
- 1 times truncation [i] based on linear OA(2²⁰⁰, 65576, F₂, 25) (dual of [65576, 65376, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. 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]
    2. linear OA(2¹⁶¹, 65537, F₂, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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 (176, 200, 13115)-net over F₂	[i]		Net Duplication
2	Digital (177, 201, 13115)-net over F₂	[i]
3	Digital (178, 202, 13115)-net over F₂	[i]
4	Digital (179, 203, 13115)-net over F₂	[i]