MinT - Information on Result #1215573

Information on Result #1215573

Digital (146, 164, 1864394)-net over F₈, using (u,Â u+v)-construction based on

digital (17, 26, 260)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (4, 8, 130)-net over F₈, using
    - trace code for nets [i] based on digital (0, 4, 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]
  2. digital (9, 18, 130)-net over F₈, using
    - trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
digital (120, 138, 1864134)-net over F₈, using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁶⁹, 932067, F₆₄, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
    - OA 9-folding and stacking [i] based on linear OA(64⁶⁹, large, F₆₄, 18) (dual of [large, large−69, 19]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (147, 165, 1864394)-net over F₈	[i]		Net Duplication