MinT - Information on Result #1185228

Information on Result #1185228

Digital (140, 165, 4922)-net over F₃, using net defined by OOA based on linear OOA(3¹⁶⁵, 4922, F₃, 25, 25) (dual of [(4922, 25), 122885, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(3¹⁶⁵, 59065, F₃, 25) (dual of [59065, 58900, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁶⁵, 59073, F₃, 25) (dual of [59073, 58908, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
    1. linear OA(3¹⁶¹, 59049, F₃, 25) (dual of [59049, 58888, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3⁴, 24, F₃, 2) (dual of [24, 20, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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 (141, 165, 4922)-net over F₃	[i]	t-Expansion
2	Digital (141, 166, 4922)-net over F₃	[i]	Net Duplication
3	Digital (142, 167, 4922)-net over F₃	[i]	Net Duplication
4	Digital (140, 164, 4922)-net over F₃	[i]	m-Reduction