MinT - Information on Result #1763671

Information on Result #1763671

Digital (119, 137, 63202)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁷, 63202, F₃, 2, 18) (dual of [(63202, 2), 126267, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁷, 88587, F₃, 2, 18) (dual of [(88587, 2), 177037, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹³⁵, 88586, F₃, 2, 18) (dual of [(88586, 2), 177037, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹³⁵, 177172, F₃, 18) (dual of [177172, 177037, 19]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹³⁴, 177171, F₃, 18) (dual of [177171, 177037, 19]-code), using
      - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(15) [i] based on
        linear OA(3¹³³, 177147, F₃, 19) (dual of [177147, 177014, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(3²³, 24, F₃, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
        dual of repetition code with length 24 [i]
        linear OA(3¹, 24, F₃, 1) (dual of [24, 23, 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.