MinT - Best Known (77, 152, s)-Nets in Base 8

Best Known (77, 152, s)-Nets in Base 8

(77, 152, 160)-Net over F₈ — Constructive and digital

Digital (77, 152, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 76, 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]

(77, 152, 260)-Net over F₈ — Digital

Digital (77, 152, 260)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 152, 10125)-Net in Base 8 — Upper bound on s

There is no (77, 152, 10126)-net in base 8, because

1 times m-reduction [i] would yield (77, 151, 10126)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23333 370961 372357 596496 930026 020294 995506 613921 125374 733073 875951 030834 889278 099386 391282 397466 937027 967051 519068 593039 802223 170971 340308 > 8¹⁵¹ [i]