MinT - Information on Result #1754565

Information on Result #1754565

Digital (172, 190, 349529)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁰, 349529, F₂, 6, 18) (dual of [(349529, 6), 2096984, 19]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁹⁰, 2097174, F₂, 18) (dual of [2097174, 2096984, 19]-code), using
- 1 times truncation [i] based on linear OA(2¹⁹¹, 2097175, F₂, 19) (dual of [2097175, 2096984, 20]-code), using
  - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹⁹⁰, 2097152, F₂, 19) (dual of [2097152, 2096962, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹⁶⁹, 2097152, F₂, 17) (dual of [2097152, 2096983, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
      - strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
        dual of repetition code with length 23 [i]
    4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 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 (173, 191, 349529)-net over F₂	[i]		Net Duplication
2	Digital (174, 192, 349529)-net over F₂	[i]
3	Digital (175, 193, 349529)-net over F₂	[i]
4	Digital (176, 194, 349529)-net over F₂	[i]