MinT - Information on Result #1224571

Information on Result #1224571

Digital (40, 47, large)-net over F₃₂, using (u,Â u+v)-construction based on

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]
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 (41, 47, large)-net over F₃₂	[i]	t-Expansion
2	Digital (42, 47, large)-net over F₃₂	[i]
3	Digital (43, 47, large)-net over F₃₂	[i]
4	Digital (44, 47, large)-net over F₃₂	[i]
5	Digital (41, 48, large)-net over F₃₂	[i]	Net Duplication
6	Digital (42, 49, large)-net over F₃₂	[i]
7	Digital (43, 50, large)-net over F₃₂	[i]
8	Digital (44, 51, large)-net over F₃₂	[i]
9	Digital (45, 52, large)-net over F₃₂	[i]
10	Digital (46, 53, large)-net over F₃₂	[i]
11	Digital (47, 54, large)-net over F₃₂	[i]
12	Digital (40, 46, large)-net over F₃₂	[i]	m-Reduction
13	Digital (40, 45, large)-net over F₃₂	[i]
14	Digital (40, 44, large)-net over F₃₂	[i]
15	Digital (40, 43, large)-net over F₃₂	[i]