MinT - Best Known (33, 33+69, s)-Nets in Base 8

Best Known (33, 33+69, s)-Nets in Base 8

(33, 33+69, 65)-Net over F₈ — Constructive and digital

Digital (33, 102, 65)-net over F₈, using

t-expansion [i] based on digital (14, 102, 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+69, 97)-Net over F₈ — Digital

Digital (33, 102, 97)-net over F₈, using

t-expansion [i] based on digital (28, 102, 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+69, 910)-Net in Base 8 — Upper bound on s

There is no (33, 102, 911)-net in base 8, because

1 times m-reduction [i] would yield (33, 101, 911)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 850610 385072 558239 834865 924699 416324 989539 359975 834770 015768 575416 166068 669270 519820 706460 > 8¹⁰¹ [i]