MinT - Best Known (112−53, 112, s)-Nets in Base 8

Best Known (112−53, 112, s)-Nets in Base 8

(112−53, 112, 208)-Net over F₈ — Constructive and digital

Digital (59, 112, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 56, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(112−53, 112, 240)-Net over F₈ — Digital

Digital (59, 112, 240)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−53, 112, 10790)-Net in Base 8 — Upper bound on s

There is no (59, 112, 10791)-net in base 8, because

1 times m-reduction [i] would yield (59, 111, 10791)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17517 817642 446076 954469 535001 771162 146180 780928 746711 287669 154146 131268 462934 134916 493004 707608 517580 > 8¹¹¹ [i]