MinT - Best Known (149−117, 149, s)-Nets in Base 8

Best Known (149−117, 149, s)-Nets in Base 8

(149−117, 149, 65)-Net over F₈ — Constructive and digital

Digital (32, 149, 65)-net over F₈, using

t-expansion [i] based on digital (14, 149, 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]

(149−117, 149, 97)-Net over F₈ — Digital

Digital (32, 149, 97)-net over F₈, using

t-expansion [i] based on digital (28, 149, 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]

(149−117, 149, 610)-Net in Base 8 — Upper bound on s

There is no (32, 149, 611)-net in base 8, because

1 times m-reduction [i] would yield (32, 148, 611)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48 245825 924615 143405 973806 481917 825384 124420 860809 646355 946694 333273 536214 482318 909606 077130 790263 099753 670003 681449 067095 206350 459464 > 8¹⁴⁸ [i]