MinT - Information on Result #1752578

Information on Result #1752578

Digital (137, 158, 6561)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁸, 6561, F₂, 5, 21) (dual of [(6561, 5), 32647, 22]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁵⁸, 32805, F₂, 21) (dual of [32805, 32647, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁵⁸, 32806, F₂, 21) (dual of [32806, 32648, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(2¹⁵¹, 32769, F₂, 21) (dual of [32769, 32618, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(2¹²¹, 32769, F₂, 17) (dual of [32769, 32648, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’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, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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 (138, 159, 6561)-net over F₂	[i]		Net Duplication
2	Digital (139, 160, 6561)-net over F₂	[i]		Net Duplication