MinT - Best Known (33, 33+109, s)-Nets in Base 8

Best Known (33, 33+109, s)-Nets in Base 8

(33, 33+109, 65)-Net over F₈ — Constructive and digital

Digital (33, 142, 65)-net over F₈, using

t-expansion [i] based on digital (14, 142, 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+109, 97)-Net over F₈ — Digital

Digital (33, 142, 97)-net over F₈, using

t-expansion [i] based on digital (28, 142, 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+109, 649)-Net in Base 8 — Upper bound on s

There is no (33, 142, 650)-net in base 8, because

1 times m-reduction [i] would yield (33, 141, 650)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 641697 958657 397292 175656 630683 734262 963084 612278 800105 741332 277201 147784 930361 523435 670328 991069 410970 322023 962031 957869 948064 > 8¹⁴¹ [i]