MinT - Best Known (90, 90+66, s)-Nets in Base 8

Best Known (90, 90+66, s)-Nets in Base 8

(90, 90+66, 354)-Net over F₈ — Constructive and digital

Digital (90, 156, 354)-net over F₈, using

10 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(90, 90+66, 514)-Net over F₈ — Digital

Digital (90, 156, 514)-net over F₈, using

trace code for nets [i] based on digital (12, 78, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(90, 90+66, 34926)-Net in Base 8 — Upper bound on s

There is no (90, 156, 34927)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 724530 976495 324963 885054 198329 486870 164084 962391 356999 635822 729268 943192 505277 184454 724016 925967 336968 172800 761054 050375 333327 931923 677326 > 8¹⁵⁶ [i]