MinT - Best Known (33, 33+134, s)-Nets in Base 8

Best Known (33, 33+134, s)-Nets in Base 8

(33, 33+134, 65)-Net over F₈ — Constructive and digital

Digital (33, 167, 65)-net over F₈, using

t-expansion [i] based on digital (14, 167, 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]

(33, 33+134, 97)-Net over F₈ — Digital

Digital (33, 167, 97)-net over F₈, using

t-expansion [i] based on digital (28, 167, 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]

(33, 33+134, 614)-Net in Base 8 — Upper bound on s

There is no (33, 167, 615)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 696191 561108 260233 200690 347970 997464 026329 321736 038136 244975 070912 516116 124355 462031 518981 883309 786348 056356 202651 036478 630560 682352 179688 596875 543756 > 8¹⁶⁷ [i]