MinT - Information on Result #1765058

Information on Result #1765058

Digital (138, 161, 25767)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶¹, 25767, F₃, 2, 23) (dual of [(25767, 2), 51373, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶¹, 29544, F₃, 2, 23) (dual of [(29544, 2), 58927, 24]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁶⁰, 29544, F₃, 2, 23) (dual of [(29544, 2), 58928, 24]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁵⁸, 29543, F₃, 2, 23) (dual of [(29543, 2), 58928, 24]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁵⁸, 59086, F₃, 23) (dual of [59086, 58928, 24]-code), using
      - 1 times code embedding in larger space [i] based on linear OA(3¹⁵⁷, 59085, F₃, 23) (dual of [59085, 58928, 24]-code), using
        constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
        linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(3¹²¹, 59049, F₃, 19) (dual of [59049, 58928, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(3⁶, 36, F₃, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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.