MinT - Information on Result #1217194

Information on Result #1217194

Digital (55, 62, large)-net over F₉, using (u,Â u+v)-construction based on

digital (9, 12, 5580100)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹², 5580100, F₉, 3, 3) (dual of [(5580100, 3), 16740288, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(9¹², 5580100, F₉, 2, 3) (dual of [(5580100, 2), 11160188, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9¹², 5580100, F₉, 3) (dual of [5580100, 5580088, 4]-code or 5580100-cap in PG(11,9)), using
      - product of projective cap with cap in AG(5,Â 9) [i] based on linear OA(9⁷, 6723, F₉, 3) (dual of [6723, 6716, 4]-code or 6723-cap in PG(6,9)), using
        product of two caps with tangent hyperplane [i]
digital (43, 50, 5592401)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁵⁰, 5592401, F₉, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(9⁵⁰, 5592402, F₉, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
    - trace code [i] based on 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 (56, 62, large)-net over F₉	[i]		t-Expansion
2	Digital (56, 63, large)-net over F₉	[i]		Net Duplication
3	Digital (55, 61, large)-net over F₉	[i]		m-Reduction
4	Digital (55, 60, large)-net over F₉	[i]
5	Digital (55, 59, large)-net over F₉	[i]
6	Digital (55, 58, large)-net over F₉	[i]