MinT - Information on Result #1185576

Information on Result #1185576

Digital (178, 209, 3939)-net over F₃, using net defined by OOA based on linear OOA(3²⁰⁹, 3939, F₃, 31, 31) (dual of [(3939, 31), 121900, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(3²⁰⁹, 59086, F₃, 31) (dual of [59086, 58877, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3²⁰⁹, 59087, F₃, 31) (dual of [59087, 58878, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(25) [i] based on
    1. linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(3¹⁷¹, 59049, F₃, 26) (dual of [59049, 58878, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(3⁸, 38, F₃, 4) (dual of [38, 30, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [i]

Mode: Constructive and 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

The following results depend on this result:

	Result		Method
1	Digital (179, 209, 3939)-net over F₃	[i]	t-Expansion
2	Digital (179, 210, 3939)-net over F₃	[i]	Net Duplication
3	Digital (180, 211, 3939)-net over F₃	[i]	Net Duplication
4	Digital (178, 208, 3939)-net over F₃	[i]	m-Reduction