MinT - Best Known (139−106, 139, s)-Nets in Base 8

Best Known (139−106, 139, s)-Nets in Base 8

(139−106, 139, 65)-Net over F₈ — Constructive and digital

Digital (33, 139, 65)-net over F₈, using

t-expansion [i] based on digital (14, 139, 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]

(139−106, 139, 97)-Net over F₈ — Digital

Digital (33, 139, 97)-net over F₈, using

t-expansion [i] based on digital (28, 139, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(139−106, 139, 654)-Net in Base 8 — Upper bound on s

There is no (33, 139, 655)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 358328 901614 169190 988862 149779 332995 077017 854393 409036 437282 871104 897860 209936 865413 661771 008283 528629 578226 600404 813073 188816 > 8¹³⁹ [i]