MinT - Best Known (50, 50+48, s)-Nets in Base 8

Best Known (50, 50+48, s)-Nets in Base 8

(50, 50+48, 160)-Net over F₈ — Constructive and digital

Digital (50, 98, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 49, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(50, 50+48, 187)-Net over F₈ — Digital

Digital (50, 98, 187)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+48, 6806)-Net in Base 8 — Upper bound on s

There is no (50, 98, 6807)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31871 600590 924340 105473 540902 976550 395737 599789 734385 893730 586099 308647 371021 285659 999344 > 8⁹⁸ [i]