MinT - Information on Result #1224519

Information on Result #1224519

Digital (11, 15, 524323)-net over F₃₂, using (u,Â u+v)-construction based on

digital (0, 2, 33)-net over F₃₂, using
- kÂ =Â 2 construction [i]
digital (9, 13, 524290)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32¹³, 524290, F₃₂, 4, 4) (dual of [(524290, 4), 2097147, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(32¹³, 1048580, F₃₂, 4) (dual of [1048580, 1048567, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(32⁹, 1048576, F₃₂, 3) (dual of [1048576, 1048567, 4]-code or 1048576-cap in PG(8,32)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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 (43, 51, 2621473)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets
2	Digital (47, 56, 2621473)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets
3	Digital (89, 102, 3320523)-net over F₃₂	[i]		Generalized (u,Â u+v)-Construction for Nets
4	Digital (85, 97, 3320523)-net over F₃₂	[i]		Generalized (u,Â u+v)-Construction for Nets