MinT - Information on Result #1193026

Information on Result #1193026

Digital (26, 31, 2391497)-net over F₉, using net defined by OOA based on linear OOA(9³¹, 2391497, F₉, 6, 5) (dual of [(2391497, 6), 14348951, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9³¹, 2391498, F₉, 2, 5) (dual of [(2391498, 2), 4782965, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9², 10, F₉, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;18,9) [i]
  2. linear OOA(9²⁹, 2391488, F₉, 2, 5) (dual of [(2391488, 2), 4782947, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9²⁹, 4782976, F₉, 5) (dual of [4782976, 4782947, 6]-code), using
      - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(9²⁹, 4782969, F₉, 5) (dual of [4782969, 4782940, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(9²², 4782969, F₉, 4) (dual of [4782969, 4782947, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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 (95, 105, 5746937)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (102, 113, 5746937)-net over F₉	[i]		(u,Â u+v)-Construction for Nets