MinT - Best Known (53, 53+51, s)-Nets in Base 8

Best Known (53, 53+51, s)-Nets in Base 8

(53, 53+51, 160)-Net over F₈ — Constructive and digital

Digital (53, 104, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 52, 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]

(53, 53+51, 195)-Net over F₈ — Digital

Digital (53, 104, 195)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+51, 7627)-Net in Base 8 — Upper bound on s

There is no (53, 104, 7628)-net in base 8, because

1 times m-reduction [i] would yield (53, 103, 7628)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1045 200499 828922 244136 923006 710684 852230 677465 767623 654908 504909 679906 855552 663807 580809 884828 > 8¹⁰³ [i]