MinT - Information on Result #1210408

Information on Result #1210408

Digital (139, 154, 1198566)-net over F₄, using (u,Â u+v)-construction based on

digital (14, 21, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]
digital (118, 133, 1198371)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹³³, 1198371, F₄, 15, 15) (dual of [(1198371, 15), 17975432, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(4¹³³, 8388598, F₄, 15) (dual of [8388598, 8388465, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (140, 155, 1198566)-net over F₄	[i]		Net Duplication
2	Digital (141, 156, 1198566)-net over F₄	[i]		Net Duplication