MinT - Best Known (37, 37+69, s)-Nets in Base 8

Best Known (37, 37+69, s)-Nets in Base 8

(37, 37+69, 98)-Net over F₈ — Constructive and digital

Digital (37, 106, 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+69, 121)-Net over F₈ — Digital

Digital (37, 106, 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+69, 1168)-Net in Base 8 — Upper bound on s

There is no (37, 106, 1169)-net in base 8, because

1 times m-reduction [i] would yield (37, 105, 1169)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 68351 961547 313085 850230 751559 702203 421288 253230 116127 628774 578356 752297 216482 057679 627912 834720 > 8¹⁰⁵ [i]