MinT - Information on Result #1081347

Information on Result #1081347

Linear OOA(3²¹⁵, 2097314, F₃, 4, 19) (dual of [(2097314, 4), 8389041, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁴, 164, F₃, 4, 9) (dual of [(164, 4), 622, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (25, 34, 164)-net over F₃, using
  - trace code for nets [i] based on digital (8, 17, 82)-net over F₉, using
    - base reduction for projective spaces (embedding PG(8,81) in PG(16,9)) for nets [i] based on digital (0, 9, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
linear OOA(3¹⁸¹, 2097150, F₃, 4, 19) (dual of [(2097150, 4), 8388419, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁵, 2097314, F₃, 4, 18) (dual of [(2097314, 4), 8389041, 19]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²¹⁶, 2097314, F₃, 4, 19) (dual of [(2097314, 4), 8389040, 20]-NRT-code)	[i]		OOA Duplication