MinT - Information on Result #1762988

Information on Result #1762988

Digital (106, 124, 24382)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²⁴, 24382, F₃, 2, 18) (dual of [(24382, 2), 48640, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²⁴, 29536, F₃, 2, 18) (dual of [(29536, 2), 58948, 19]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹²³, 29536, F₃, 2, 18) (dual of [(29536, 2), 58949, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹²³, 59072, F₃, 18) (dual of [59072, 58949, 19]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹²², 59071, F₃, 18) (dual of [59071, 58949, 19]-code), using
      - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(15) [i] based on
        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(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(3²¹, 22, F₃, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
        dual of repetition code with length 22 [i]
        linear OA(3¹, 22, F₃, 1) (dual of [22, 21, 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.