MinT - Information on Result #1221854

Information on Result #1221854

Digital (38, 44, large)-net over F₂₇, using (u,Â u+v)-construction based on

digital (6, 9, large)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁹, large, F₂₇, 3, 3), using
  - appending kth column [i] based on linear OOA(27⁹, large, F₂₇, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁹, large, F₂₇, 3) (dual of [large, large−9, 4]-code), using
      - product of projective cap with (hyper)oval [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]
digital (29, 35, 5592402)-net over F₂₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 9, large)-net over F₂₇ (see above)
  2. 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 (39, 44, large)-net over F₂₇	[i]		t-Expansion
2	Digital (39, 45, large)-net over F₂₇	[i]		Net Duplication
3	Digital (38, 43, large)-net over F₂₇	[i]		m-Reduction
4	Digital (38, 42, large)-net over F₂₇	[i]
5	Digital (38, 41, large)-net over F₂₇	[i]