MinT - Best Known (31, 31+135, s)-Nets in Base 8

Best Known (31, 31+135, s)-Nets in Base 8

(31, 31+135, 65)-Net over F₈ — Constructive and digital

Digital (31, 166, 65)-net over F₈, using

t-expansion [i] based on digital (14, 166, 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+135, 97)-Net over F₈ — Digital

Digital (31, 166, 97)-net over F₈, using

t-expansion [i] based on digital (28, 166, 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+135, 575)-Net in Base 8 — Upper bound on s

There is no (31, 166, 576)-net in base 8, because

1 times m-reduction [i] would yield (31, 165, 576)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 110191 751811 231265 977382 691279 366930 923768 604486 249263 597995 144729 961465 808899 469328 866670 458296 568183 761135 340529 841041 382752 831863 767435 212092 926856 > 8¹⁶⁵ [i]