MinT - Best Known (99−66, 99, s)-Nets in Base 8

Best Known (99−66, 99, s)-Nets in Base 8

(99−66, 99, 65)-Net over F₈ — Constructive and digital

Digital (33, 99, 65)-net over F₈, using

t-expansion [i] based on digital (14, 99, 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]

(99−66, 99, 97)-Net over F₈ — Digital

Digital (33, 99, 97)-net over F₈, using

t-expansion [i] based on digital (28, 99, 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]

(99−66, 99, 942)-Net in Base 8 — Upper bound on s

There is no (33, 99, 943)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 261716 567442 193376 683847 669250 546774 627669 046913 999675 450533 483500 030438 626556 244606 458618 > 8⁹⁹ [i]