MinT - Best Known (94, 164, s)-Nets in Base 8

Best Known (94, 164, s)-Nets in Base 8

(94, 164, 354)-Net over F₈ — Constructive and digital

Digital (94, 164, 354)-net over F₈, using

t-expansion [i] based on digital (93, 164, 354)-net over F₈, using
- 8 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(94, 164, 514)-Net over F₈ — Digital

Digital (94, 164, 514)-net over F₈, using

trace code for nets [i] based on digital (12, 82, 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]

(94, 164, 33845)-Net in Base 8 — Upper bound on s

There is no (94, 164, 33846)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12788 837763 101136 353915 053246 292952 841093 359054 945138 465816 111427 482535 164355 308767 005020 372493 720013 773274 237705 960700 919121 668435 433915 400277 648514 > 8¹⁶⁴ [i]