MinT - Information on Result #1193852

Information on Result #1193852

Digital (51, 66, 8436)-net over F₉, using net defined by OOA based on linear OOA(9⁶⁶, 8436, F₉, 15, 15) (dual of [(8436, 15), 126474, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(9⁶⁶, 59053, F₉, 15) (dual of [59053, 58987, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁶⁶, 59054, F₉, 15) (dual of [59054, 58988, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(9⁶⁶, 59049, F₉, 15) (dual of [59049, 58983, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(9⁶¹, 59049, F₉, 14) (dual of [59049, 58988, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (58, 73, 8446)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
2	Digital (59, 74, 8452)-net over F₉	[i]
3	Digital (60, 75, 8456)-net over F₉	[i]
4	Digital (61, 76, 8464)-net over F₉	[i]
5	Digital (62, 77, 8466)-net over F₉	[i]
6	Digital (63, 78, 8468)-net over F₉	[i]
7	(63, 78, 8474)-net in base 9	[i]