MinT - Best Known (88, 88+78, s)-Nets in Base 8

Best Known (88, 88+78, s)-Nets in Base 8

(88, 88+78, 256)-Net over F₈ — Constructive and digital

Digital (88, 166, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 83, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(88, 88+78, 344)-Net over F₈ — Digital

Digital (88, 166, 344)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+78, 15330)-Net in Base 8 — Upper bound on s

There is no (88, 166, 15331)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 819593 625085 351865 270981 410234 564545 233527 523884 256548 108530 783077 982066 469953 856024 443293 043881 617823 724842 123398 503045 434629 940878 543915 420906 065984 > 8¹⁶⁶ [i]