MinT - Information on Result #1194696

Information on Result #1194696

Digital (111, 142, 3938)-net over F₉, using net defined by OOA based on linear OOA(9¹⁴², 3938, F₉, 31, 31) (dual of [(3938, 31), 121936, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(9¹⁴², 59071, F₉, 31) (dual of [59071, 58929, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹⁴², 59075, F₉, 31) (dual of [59075, 58933, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(25) [i] based on
    1. linear OA(9¹³⁶, 59049, F₉, 31) (dual of [59049, 58913, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(9¹¹⁶, 59049, F₉, 26) (dual of [59049, 58933, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(9⁶, 26, F₉, 4) (dual of [26, 20, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁶, 72, F₉, 4) (dual of [72, 66, 5]-code), using
        1 times truncation [i] based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [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 (112, 143, 3938)-net over F₉	[i]	Net Duplication
2	Digital (113, 144, 3938)-net over F₉	[i]
3	Digital (114, 145, 3938)-net over F₉	[i]