MinT - Information on Result #1229533

Information on Result #1229533

Digital (124, 139, 1198496)-net over F₅, using (u,Â u+v)-construction based on

digital (12, 19, 125)-net over F₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 1, 25)-net over F₅, using
    - s-reduction based on digital (0, 1, s)-net over F₅ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  2. digital (0, 1, 25)-net over F₅ (see above)
  3. digital (1, 3, 25)-net over F₅, using
    - s-reduction based on digital (1, 3, 31)-net over F₅, using
      - kÂ =Â 2 construction [i]
  4. digital (1, 4, 25)-net over F₅, using
    - s-reduction based on digital (1, 4, 26)-net over F₅, using
      - net defined by OOA [i] based on linear OOA(5⁴, 26, F₅, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(5⁴, 26, F₅, 2, 3) (dual of [(26, 2), 48, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
  5. digital (3, 10, 25)-net over F₅, using
    - linear code embedding found in a computer search [i]
digital (105, 120, 1198371)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹²⁰, 1198371, F₅, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(5¹²⁰, 8388598, F₅, 15) (dual of [8388598, 8388478, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹²⁰, large, F₅, 15) (dual of [large, large−120, 16]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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, 140, 1198496)-net over F₅	[i]		Net Duplication