MinT - Best Known (37, 37+59, s)-Nets in Base 8

Best Known (37, 37+59, s)-Nets in Base 8

(37, 37+59, 98)-Net over F₈ — Constructive and digital

Digital (37, 96, 98)-net over F₈, using

net from sequence [i] based on digital (37, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(37, 37+59, 121)-Net over F₈ — Digital

Digital (37, 96, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 37+59, 1496)-Net in Base 8 — Upper bound on s

There is no (37, 96, 1497)-net in base 8, because

1 times m-reduction [i] would yield (37, 95, 1497)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 216456 778453 833518 876191 317176 188635 790279 087495 405972 261126 266278 354375 060950 230592 > 8⁹⁵ [i]