MinT - Best Known (136−110, 136, s)-Nets in Base 8

Best Known (136−110, 136, s)-Nets in Base 8

(136−110, 136, 65)-Net over F₈ — Constructive and digital

Digital (26, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(136−110, 136, 86)-Net over F₈ — Digital

Digital (26, 136, 86)-net over F₈, using

t-expansion [i] based on digital (25, 136, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(136−110, 136, 487)-Net in Base 8 — Upper bound on s

There is no (26, 136, 488)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 718 445753 795855 076448 296130 545030 098055 536103 301932 553907 042114 024196 057024 453652 203346 270808 089989 781326 375358 281646 881372 > 8¹³⁶ [i]