MinT - Information on Result #2796975

Information on Result #2796975

Linear OOA(3¹⁴⁸, large, F₃, 4, 7), using 13 times NRT-code embedding in larger space based on linear OOA(3⁹⁶, large, F₃, 4, 7), using

extracting embedded OOA [i] based on digital (89, 96, large)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 4)-net over F₃, using
    - net from sequence [i] based on digital (0, 3)-sequence over F₃, using
      - Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 0 and N(F) ≥ 4, using
        the rational function field F₃(x) [i]
      - Niederreiter sequence [i]
  2. digital (86, 93, 8388600)-net over F₃, using
    - trace code for nets [i] based on 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		This result only	Method
1	Linear OOA(3¹⁴⁹, large, F₃, 4, 7)	[i]		OOA Duplication
2	Linear OOA(3¹⁵⁰, large, F₃, 4, 7)	[i]
3	Linear OOA(3¹⁵¹, large, F₃, 4, 7)	[i]