MinT - Best Known (33, 33+122, s)-Nets in Base 8

Best Known (33, 33+122, s)-Nets in Base 8

(33, 33+122, 65)-Net over F₈ — Constructive and digital

Digital (33, 155, 65)-net over F₈, using

t-expansion [i] based on digital (14, 155, 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+122, 97)-Net over F₈ — Digital

Digital (33, 155, 97)-net over F₈, using

t-expansion [i] based on digital (28, 155, 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+122, 625)-Net in Base 8 — Upper bound on s

There is no (33, 155, 626)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 99 910797 788859 839128 829145 725277 385454 153490 780758 076250 942722 024268 432037 388572 513486 988597 846539 586668 004704 150093 220473 675339 456884 527408 > 8¹⁵⁵ [i]