MinT - Information on Result #3241119

Information on Result #3241119

Digital (44, 49, large)-net over F₂₇, using t-expansion based on digital (42, 49, large)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. 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]
2. digital (33, 40, 5592400)-net over F₂₇, using
  - (u,Â u+v)-construction [i] based on
    1. digital (6, 9, large)-net over F₂₇ (see above)
    2. digital (24, 31, 2796200)-net over F₂₇, using
      - net defined by OOA [i] based on linear OOA(27³¹, 2796200, F₂₇, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
        OOA 3-folding and stacking with additional row [i] based on linear OA(27³¹, 8388601, F₂₇, 7) (dual of [8388601, 8388570, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’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		Method
1	Digital (45, 50, large)-net over F₂₇	[i]	Net Duplication
2	Digital (46, 51, large)-net over F₂₇	[i]
3	Digital (47, 52, large)-net over F₂₇	[i]
4	Digital (48, 53, large)-net over F₂₇	[i]
5	Digital (49, 54, large)-net over F₂₇	[i]
6	Digital (50, 55, large)-net over F₂₇	[i]
7	Digital (51, 56, large)-net over F₂₇	[i]
8	Digital (52, 57, large)-net over F₂₇	[i]
9	Digital (53, 58, large)-net over F₂₇	[i]
10	Digital (54, 59, large)-net over F₂₇	[i]