MinT - Information on Result #1753144

Information on Result #1753144

Digital (141, 168, 1328)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁸, 1328, F₂, 3, 27) (dual of [(1328, 3), 3816, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁶⁸, 1377, F₂, 3, 27) (dual of [(1377, 3), 3963, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶⁵, 1376, F₂, 3, 27) (dual of [(1376, 3), 3963, 28]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁶⁵, 4128, F₂, 27) (dual of [4128, 3963, 28]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹⁶³, 4126, F₂, 27) (dual of [4126, 3963, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
        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(2¹³³, 4096, F₂, 23) (dual of [4096, 3963, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.