MinT - Information on Result #3242578

Information on Result #3242578

Digital (44, 47, large)-net over F₃₂, using t-expansion based on digital (40, 47, large)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 8, 3214400)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32⁸, 3214400, F₃₂, 3, 3) (dual of [(3214400, 3), 9643192, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(32⁸, 3214400, F₃₂, 2, 3) (dual of [(3214400, 2), 6428792, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(32⁸, 3214400, F₃₂, 3) (dual of [3214400, 3214392, 4]-code or 3214400-cap in PG(7,32)), using
        product of projective cap with cap in AG(4,Â 32) [i] based on linear OA(32⁴, 1025, F₃₂, 3) (dual of [1025, 1021, 4]-code or 1025-cap in PG(3,32)), using
        ovoid in PG(3,Â 32) [i]
2. digital (32, 39, 5592400)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (5, 8, 3214400)-net over F₃₂ (see above)
    2. digital (24, 31, 2796200)-net over F₃₂, using
      - net defined by OOA [i] based on linear OOA(32³¹, 2796200, F₃₂, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
        OOA 3-folding and stacking with additional row [i] based on linear OA(32³¹, 8388601, F₃₂, 7) (dual of [8388601, 8388570, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(32³¹, large, F₃₂, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (45, 48, large)-net over F₃₂	[i]	Net Duplication
2	Digital (46, 49, large)-net over F₃₂	[i]
3	Digital (47, 50, large)-net over F₃₂	[i]