MinT - Information on Result #3174555

Information on Result #3174555

Digital (57, 61, large)-net over F₉, using 3 times m-reduction based on digital (57, 64, large)-net over F₉, using

trace code for nets [i] based on digital (25, 32, 5592401)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81³², 5592401, F₈₁, 9, 7) (dual of [(5592401, 9), 50331577, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(81³², 5592402, F₈₁, 3, 7) (dual of [(5592402, 3), 16777174, 8]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(81⁷, large, F₈₁, 3, 3), using
        appending kth column [i] based on linear OOA(81⁷, large, F₈₁, 2, 3), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁷, large, F₈₁, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 81²-ovoid cap in AG(3,Â 81) [i] based on linear OA(81⁴, 6562, F₈₁, 3) (dual of [6562, 6558, 4]-code or 6562-cap in PG(3,81)), using
        ovoid in PG(3,Â 81) [i]
      2. linear OOA(81²⁵, 2796201, F₈₁, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81²⁵, large, F₈₁, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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		This result only	Method
1	Digital (58, 61, large)-net over F₉	[i]		t-Expansion