MinT - Information on Result #1184656

Information on Result #1184656

Digital (106, 125, 6563)-net over F₃, using net defined by OOA based on linear OOA(3¹²⁵, 6563, F₃, 19, 19) (dual of [(6563, 19), 124572, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(3¹²⁵, 59068, F₃, 19) (dual of [59068, 58943, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹²⁵, 59073, F₃, 19) (dual of [59073, 58948, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
    1. 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]
    2. 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]
    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 (107, 125, 6563)-net over F₃	[i]	t-Expansion
2	Digital (107, 126, 6563)-net over F₃	[i]	Net Duplication
3	Digital (108, 127, 6563)-net over F₃	[i]	Net Duplication
4	Digital (106, 124, 6563)-net over F₃	[i]	m-Reduction