MinT - Information on Result #1222231

Information on Result #1222231

Digital (63, 77, 1198437)-net over F₂₇, using (u,Â u+v)-construction based on

digital (4, 11, 66)-net over F₂₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 28)-net over F₂₇, using
    - net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 8, 38)-net over F₂₇, using
    - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
digital (52, 66, 1198371)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁶⁶, 1198371, F₂₇, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(27⁶⁶, 8388597, F₂₇, 14) (dual of [8388597, 8388531, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁶⁶, large, F₂₇, 14) (dual of [large, large−66, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (94, 108, 2396874)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets