MinT - Information on Result #1754692

Information on Result #1754692

Digital (161, 192, 1359)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹², 1359, F₂, 3, 31) (dual of [(1359, 3), 3885, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹², 1377, F₂, 3, 31) (dual of [(1377, 3), 3939, 32]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁹, 1376, F₂, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁸⁹, 4128, F₂, 31) (dual of [4128, 3939, 32]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹⁸⁷, 4126, F₂, 31) (dual of [4126, 3939, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
        linear OA(2¹⁸¹, 4096, F₂, 31) (dual of [4096, 3915, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [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

None.