MinT - Best Known (31, 31+105, s)-Nets in Base 8

Best Known (31, 31+105, s)-Nets in Base 8

(31, 31+105, 65)-Net over F₈ — Constructive and digital

Digital (31, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 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]

(31, 31+105, 97)-Net over F₈ — Digital

Digital (31, 136, 97)-net over F₈, using

t-expansion [i] based on digital (28, 136, 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]

(31, 31+105, 606)-Net in Base 8 — Upper bound on s

There is no (31, 136, 607)-net in base 8, because

1 times m-reduction [i] would yield (31, 135, 607)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 86 996023 753575 250443 354644 066251 861005 817153 468638 618400 833784 049532 198114 595519 540038 438464 973851 514457 203134 206955 144166 > 8¹³⁵ [i]