MinT - Best Known (102−65, 102, s)-Nets in Base 8

Best Known (102−65, 102, s)-Nets in Base 8

(102−65, 102, 98)-Net over F₈ — Constructive and digital

Digital (37, 102, 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]

(102−65, 102, 121)-Net over F₈ — Digital

Digital (37, 102, 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]

(102−65, 102, 1274)-Net in Base 8 — Upper bound on s

There is no (37, 102, 1275)-net in base 8, because

1 times m-reduction [i] would yield (37, 101, 1275)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 419007 933375 373526 681500 544694 123174 590405 129864 023040 628279 233969 016768 183540 318206 536193 > 8¹⁰¹ [i]