MinT - Information on Result #1757344

Information on Result #1757344

Digital (205, 227, 174770)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²⁷, 174770, F₂, 6, 22) (dual of [(174770, 6), 1048393, 23]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²²⁷, 1048620, F₂, 22) (dual of [1048620, 1048393, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2²²⁷, 1048622, F₂, 22) (dual of [1048622, 1048395, 23]-code), using
  - 1 times truncation [i] based on linear OA(2²²⁸, 1048623, F₂, 23) (dual of [1048623, 1048395, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
      1. linear OA(2²²¹, 1048576, F₂, 23) (dual of [1048576, 1048355, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁸¹, 1048576, F₂, 19) (dual of [1048576, 1048395, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(2⁷, 47, F₂, 3) (dual of [47, 40, 4]-code or 47-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 (206, 228, 174770)-net over F₂	[i]		Net Duplication
2	Digital (207, 229, 174770)-net over F₂	[i]
3	Digital (208, 230, 174770)-net over F₂	[i]