MinT - Best Known (156−119, 156, s)-Nets in Base 8

Best Known (156−119, 156, s)-Nets in Base 8

(156−119, 156, 98)-Net over F₈ — Constructive and digital

Digital (37, 156, 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]

(156−119, 156, 121)-Net over F₈ — Digital

Digital (37, 156, 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]

(156−119, 156, 731)-Net in Base 8 — Upper bound on s

There is no (37, 156, 732)-net in base 8, because

1 times m-reduction [i] would yield (37, 155, 732)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 96 532553 767467 797722 028573 562839 813140 952180 245342 318715 741323 883968 486404 030786 147183 438919 346984 016478 374472 717448 652856 918482 876049 980290 > 8¹⁵⁵ [i]