MinT - Information on Result #1207994

Information on Result #1207994

Digital (148, 159, 5033167)-net over F₃, using (u,Â u+v)-construction based on

digital (1, 6, 7)-net over F₃, using
- net from sequence [i] based on digital (1, 6)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
digital (142, 153, 5033160)-net over F₃, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27⁵¹, 1677720, F₂₇, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(27⁵¹, 8388601, F₂₇, 11) (dual of [8388601, 8388550, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁵¹, large, F₂₇, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁵⁹, 5033167, F₃, 4, 11) (dual of [(5033167, 4), 20132509, 12]-NRT-code)	[i]		Extracting Embedded OOA
2	Linear OOA(3¹⁵⁹, 5033167, F₃, 5, 11) (dual of [(5033167, 5), 25165676, 12]-NRT-code)	[i]		Extracting Embedded OOA