MinT - Best Known (135−98, 135, s)-Nets in Base 8

Best Known (135−98, 135, s)-Nets in Base 8

(135−98, 135, 98)-Net over F₈ — Constructive and digital

Digital (37, 135, 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]

(135−98, 135, 121)-Net over F₈ — Digital

Digital (37, 135, 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]

(135−98, 135, 809)-Net in Base 8 — Upper bound on s

There is no (37, 135, 810)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85 515730 364127 750530 499692 969818 054580 493906 211331 434037 119006 187849 698563 803512 821330 349994 180129 698650 819916 062976 612144 > 8¹³⁵ [i]