MinT - Best Known (34, 34+134, s)-Nets in Base 8

Best Known (34, 34+134, s)-Nets in Base 8

(34, 34+134, 65)-Net over F₈ — Constructive and digital

Digital (34, 168, 65)-net over F₈, using

t-expansion [i] based on digital (14, 168, 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]

(34, 34+134, 98)-Net over F₈ — Digital

Digital (34, 168, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(34, 34+134, 635)-Net in Base 8 — Upper bound on s

There is no (34, 168, 636)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 55 299738 904870 656977 459956 038404 912767 169719 313174 294066 933527 324312 086161 521220 085557 877439 458054 387002 170249 860208 882805 371462 814022 493441 970758 108881 > 8¹⁶⁸ [i]