MinT - Best Known (80−35, 80, s)-Nets in Base 8

Best Known (80−35, 80, s)-Nets in Base 8

(80−35, 80, 256)-Net over F₈ — Constructive and digital

Digital (45, 80, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 40, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(80−35, 80, 266)-Net over F₈ — Digital

Digital (45, 80, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 40, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(80−35, 80, 16116)-Net in Base 8 — Upper bound on s

There is no (45, 80, 16117)-net in base 8, because

1 times m-reduction [i] would yield (45, 79, 16117)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 220904 394104 323857 007176 038198 494381 286307 300533 878971 956826 931706 551900 > 8⁷⁹ [i]