MinT - Information on Result #1757751

Information on Result #1757751

Digital (210, 232, 299596)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³², 299596, F₂, 7, 22) (dual of [(299596, 7), 2096940, 23]-NRT-code), using

OOA 7-folding [i] based on linear OA(2²³², 2097172, F₂, 22) (dual of [2097172, 2096940, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2²³², 2097173, F₂, 22) (dual of [2097173, 2096941, 23]-code), using
  - 1 times truncation [i] based on linear OA(2²³³, 2097174, F₂, 23) (dual of [2097174, 2096941, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(2²³², 2097152, F₂, 23) (dual of [2097152, 2096920, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2²¹¹, 2097152, F₂, 21) (dual of [2097152, 2096941, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹, 22, F₂, 1) (dual of [22, 21, 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 (211, 233, 299596)-net over F₂	[i]		Net Duplication
2	Digital (212, 234, 299596)-net over F₂	[i]
3	Digital (213, 235, 299596)-net over F₂	[i]
4	Digital (214, 236, 299596)-net over F₂	[i]