MinT - Information on Result #3176958

Information on Result #3176958

Digital (35, 40, large)-net over F₂₇, using 1 times m-reduction based on digital (35, 41, large)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 532899)-net over F₂₇, using
  - s-reduction based on digital (0, 0, s)-net over F₂₇ for arbitrarily large s, using
    - arbitrary set of 27⁰ points [i]
2. digital (0, 0, 532899)-net over F₂₇ (see above)
3. digital (0, 0, 532899)-net over F₂₇ (see above)
4. digital (0, 0, 532899)-net over F₂₇ (see above)
5. digital (0, 0, 532899)-net over F₂₇ (see above)
6. digital (0, 0, 532899)-net over F₂₇ (see above)
7. digital (0, 0, 532899)-net over F₂₇ (see above)
8. digital (0, 0, 532899)-net over F₂₇ (see above)
9. digital (0, 0, 532899)-net over F₂₇ (see above)
10. digital (0, 0, 532899)-net over F₂₇ (see above)
11. digital (0, 0, 532899)-net over F₂₇ (see above)
12. digital (0, 0, 532899)-net over F₂₇ (see above)
13. digital (0, 0, 532899)-net over F₂₇ (see above)
14. digital (0, 0, 532899)-net over F₂₇ (see above)
15. digital (0, 0, 532899)-net over F₂₇ (see above)
16. digital (0, 0, 532899)-net over F₂₇ (see above)
17. digital (0, 0, 532899)-net over F₂₇ (see above)
18. digital (0, 0, 532899)-net over F₂₇ (see above)
19. digital (0, 0, 532899)-net over F₂₇ (see above)
20. digital (0, 0, 532899)-net over F₂₇ (see above)
21. digital (0, 0, 532899)-net over F₂₇ (see above)
22. digital (0, 1, 532899)-net over F₂₇, using
  - s-reduction based on digital (0, 1, s)-net over F₂₇ for arbitrarily large s, using
    - construction for strength kÂ =Â 1 [i]
23. digital (0, 1, 532899)-net over F₂₇ (see above)
24. digital (0, 1, 532899)-net over F₂₇ (see above)
25. digital (3, 5, 532899)-net over F₂₇, using
  - s-reduction based on digital (3, 5, 551881)-net over F₂₇, using
    - kÂ =Â 2 construction [i]
26. digital (4, 7, 532899)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27⁷, 532899, F₂₇, 3, 3) (dual of [(532899, 3), 1598690, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(27⁷, 532899, F₂₇, 2, 3) (dual of [(532899, 2), 1065791, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁷, 532899, F₂₇, 3) (dual of [532899, 532892, 4]-code or 532899-cap in PG(6,27)), using
        product of two caps with tangent hyperplane [i]
27. digital (20, 26, 2796201)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27²⁶, 2796201, F₂₇, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(27²⁶, large, F₂₇, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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 (36, 40, large)-net over F₂₇	[i]		t-Expansion
2	Digital (37, 40, large)-net over F₂₇	[i]		t-Expansion