MinT - Best Known (150−115, 150, s)-Nets in Base 8

Best Known (150−115, 150, s)-Nets in Base 8

(150−115, 150, 65)-Net over F₈ — Constructive and digital

Digital (35, 150, 65)-net over F₈, using

t-expansion [i] based on digital (14, 150, 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]

(150−115, 150, 112)-Net over F₈ — Digital

Digital (35, 150, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(150−115, 150, 688)-Net in Base 8 — Upper bound on s

There is no (35, 150, 689)-net in base 8, because

1 times m-reduction [i] would yield (35, 149, 689)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 387 893015 589000 821268 398138 724840 913664 677586 761571 131548 395087 960856 890924 431191 248773 482731 809404 279478 261255 115311 483072 155723 303168 > 8¹⁴⁹ [i]