MinT - Information on Result #1754422

Information on Result #1754422

Digital (166, 188, 21848)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸⁸, 21848, F₂, 6, 22) (dual of [(21848, 6), 130900, 23]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁸⁸, 131088, F₂, 22) (dual of [131088, 130900, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁸⁸, 131089, F₂, 22) (dual of [131089, 130901, 23]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁸⁹, 131090, F₂, 23) (dual of [131090, 130901, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁷¹, 131072, F₂, 21) (dual of [131072, 130901, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (167, 189, 21848)-net over F₂	[i]		Net Duplication
2	Digital (168, 190, 21848)-net over F₂	[i]
3	Digital (169, 191, 21848)-net over F₂	[i]