MinT - Information on Result #1179324

Information on Result #1179324

Digital (11, 17, 53)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷, 53, F₃, 6, 6) (dual of [(53, 6), 301, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3¹⁷, 53, F₃, 5, 6) (dual of [(53, 5), 248, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3¹², 33, F₃, 5, 6) (dual of [(33, 5), 153, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
      - linear code embedding found in a computer search [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 (125, 137, 1398153)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (147, 159, 1594378)-net over F₃	[i]
3	Digital (185, 197, 5592453)-net over F₃	[i]
4	Digital (125, 138, 1398153)-net over F₃	[i]
5	Digital (200, 213, 5592453)-net over F₃	[i]