MinT - Best Known (139−104, 139, s)-Nets in Base 8

Best Known (139−104, 139, s)-Nets in Base 8

(139−104, 139, 65)-Net over F₈ — Constructive and digital

Digital (35, 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]

(139−104, 139, 112)-Net over F₈ — Digital

Digital (35, 139, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(139−104, 139, 717)-Net in Base 8 — Upper bound on s

There is no (35, 139, 718)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 360267 233454 025777 256988 473063 049449 236218 385328 503509 766107 485544 672017 838318 687980 454774 496677 198252 390798 199110 521909 448004 > 8¹³⁹ [i]