MinT - Best Known (144−71, 144, s)-Nets in Base 8

Best Known (144−71, 144, s)-Nets in Base 8

(144−71, 144, 160)-Net over F₈ — Constructive and digital

Digital (73, 144, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 72, 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]

(144−71, 144, 249)-Net over F₈ — Digital

Digital (73, 144, 249)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−71, 144, 9703)-Net in Base 8 — Upper bound on s

There is no (73, 144, 9704)-net in base 8, because

1 times m-reduction [i] would yield (73, 143, 9704)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1386 354361 547856 916259 193945 361990 037265 421670 952623 912115 462705 082361 144963 877008 832347 668705 579888 133706 372114 978511 325454 278831 > 8¹⁴³ [i]