MinT - Best Known (79−34, 79, s)-Nets in Base 8

Best Known (79−34, 79, s)-Nets in Base 8

(79−34, 79, 256)-Net over F₈ — Constructive and digital

Digital (45, 79, 256)-net over F₈, using

1 times m-reduction [i] based on 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]

(79−34, 79, 275)-Net over F₈ — Digital

Digital (45, 79, 275)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−34, 79, 16116)-Net in Base 8 — Upper bound on s

There is no (45, 79, 16117)-net in base 8, because

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]