MinT - Information on Result #1758172

Information on Result #1758172

Digital (212, 237, 74905)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁷, 74905, F₂, 7, 25) (dual of [(74905, 7), 524098, 26]-NRT-code), using

OOA 7-folding [i] based on linear OA(2²³⁷, 524335, F₂, 25) (dual of [524335, 524098, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2²³⁶, 524334, F₂, 25) (dual of [524334, 524098, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(2²²⁹, 524289, F₂, 25) (dual of [524289, 524060, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(2¹⁹¹, 524289, F₂, 21) (dual of [524289, 524098, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’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, 45, F₂, 3) (dual of [45, 38, 4]-code or 45-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 (213, 238, 74905)-net over F₂	[i]		Net Duplication
2	Digital (214, 239, 74905)-net over F₂	[i]
3	Digital (215, 240, 74905)-net over F₂	[i]