MinT - Information on Result #1750308

Information on Result #1750308

Digital (92, 106, 8196)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰⁶, 8196, F₂, 4, 14) (dual of [(8196, 4), 32678, 15]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁰⁶, 32784, F₂, 14) (dual of [32784, 32678, 15]-code), using
- 1 times truncation [i] based on linear OA(2¹⁰⁷, 32785, F₂, 15) (dual of [32785, 32678, 16]-code), using
  - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
    1. linear OA(2¹⁰⁶, 32768, F₂, 15) (dual of [32768, 32662, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
      - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
    4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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 (93, 107, 8196)-net over F₂	[i]		Net Duplication
2	Digital (94, 108, 8196)-net over F₂	[i]
3	Digital (95, 109, 8196)-net over F₂	[i]