MinT - Best Known (50−16, 50, s)-Nets in Base 8

Best Known (50−16, 50, s)-Nets in Base 8

(50−16, 50, 354)-Net over F₈ — Constructive and digital

Digital (34, 50, 354)-net over F₈, using

4 times m-reduction [i] based on digital (34, 54, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 27, 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]

(50−16, 50, 518)-Net in Base 8 — Constructive

(34, 50, 518)-net in base 8, using

8² times duplication [i] based on (32, 48, 518)-net in base 8, using
- base change [i] based on digital (20, 36, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 18, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(50−16, 50, 947)-Net over F₈ — Digital

Digital (34, 50, 947)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(50−16, 50, 237080)-Net in Base 8 — Upper bound on s

There is no (34, 50, 237081)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1427 269018 152100 993118 679890 226252 006252 884335 > 8⁵⁰ [i]