MinT - Information on Result #1179564

Information on Result #1179564

Digital (14, 18, 29537)-net over F₉, using net defined by OOA based on linear OOA(9¹⁸, 29537, F₉, 4, 4) (dual of [(29537, 4), 118130, 5]-NRT-code), using

appending kth column [i] based on linear OOA(9¹⁸, 29537, F₉, 3, 4) (dual of [(29537, 3), 88593, 5]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9², 10, F₉, 3, 2) (dual of [(10, 3), 28, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;28,9) [i]
  2. linear OOA(9¹⁶, 29527, F₉, 3, 4) (dual of [(29527, 3), 88565, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(9¹⁶, 59054, F₉, 4) (dual of [59054, 59038, 5]-code), using
      - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(9¹⁶, 59049, F₉, 4) (dual of [59049, 59033, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(9¹¹, 59049, F₉, 3) (dual of [59049, 59038, 4]-code or 59049-cap in PG(10,9)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        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		This result only	Method
1	Digital (68, 76, 4223837)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (75, 84, 4223837)-net over F₉	[i]		(u,Â u+v)-Construction for Nets