MinT - Information on Result #1749618

Information on Result #1749618

Digital (68, 81, 2052)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁸¹, 2052, F₂, 4, 13) (dual of [(2052, 4), 8127, 14]-NRT-code), using

OOA 4-folding [i] based on linear OA(2⁸¹, 8208, F₂, 13) (dual of [8208, 8127, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2⁸⁰, 8207, F₂, 13) (dual of [8207, 8127, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2⁷⁹, 8192, F₂, 13) (dual of [8192, 8113, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2⁶⁶, 8192, F₂, 11) (dual of [8192, 8126, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
      - strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
    4. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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 (69, 82, 2052)-net over F₂	[i]		Net Duplication
2	Digital (70, 83, 2052)-net over F₂	[i]		Net Duplication