MinT - Information on Result #1761160

Information on Result #1761160

Digital (66, 76, 186951)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷⁶, 186951, F₃, 2, 10) (dual of [(186951, 2), 373826, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁷⁶, 265728, F₃, 2, 10) (dual of [(265728, 2), 531380, 11]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3⁷⁵, 265728, F₃, 2, 10) (dual of [(265728, 2), 531381, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁷⁵, 531456, F₃, 10) (dual of [531456, 531381, 11]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3⁷⁴, 531455, F₃, 10) (dual of [531455, 531381, 11]-code), using
      - constructionÂ X4 applied to C_e(9) âŠ‚ C_e(7) [i] based on
        linear OA(3⁷³, 531441, F₃, 10) (dual of [531441, 531368, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(3⁶¹, 531441, F₃, 8) (dual of [531441, 531380, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(3¹³, 14, F₃, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
        dual of repetition code with length 14 [i]
        linear OA(3¹, 14, F₃, 1) (dual of [14, 13, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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

None.