MinT - Information on Result #1194520

Information on Result #1194520

Digital (86, 111, 4921)-net over F₉, using net defined by OOA based on linear OOA(9¹¹¹, 4921, F₉, 25, 25) (dual of [(4921, 25), 122914, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(9¹¹¹, 59053, F₉, 25) (dual of [59053, 58942, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹¹, 59054, F₉, 25) (dual of [59054, 58943, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(23) [i] based on
    1. linear OA(9¹¹¹, 59049, F₉, 25) (dual of [59049, 58938, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(9¹⁰⁶, 59049, F₉, 24) (dual of [59049, 58943, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [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 (87, 112, 4921)-net over F₉	[i]	Net Duplication
2	Digital (88, 113, 4921)-net over F₉	[i]	Net Duplication
3	Digital (98, 123, 4931)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
4	Digital (99, 124, 4937)-net over F₉	[i]
5	Digital (100, 125, 4941)-net over F₉	[i]
6	Digital (101, 126, 4949)-net over F₉	[i]
7	Digital (102, 127, 4951)-net over F₉	[i]
8	Digital (103, 128, 4953)-net over F₉	[i]
9	Digital (104, 129, 4955)-net over F₉	[i]
10	Digital (105, 130, 4957)-net over F₉	[i]
11	Digital (106, 131, 4961)-net over F₉	[i]
12	(107, 132, 4969)-net in base 9	[i]