MinT - Best Known (154−117, 154, s)-Nets in Base 8

Best Known (154−117, 154, s)-Nets in Base 8

(154−117, 154, 98)-Net over F₈ — Constructive and digital

Digital (37, 154, 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]

(154−117, 154, 121)-Net over F₈ — Digital

Digital (37, 154, 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]

(154−117, 154, 737)-Net in Base 8 — Upper bound on s

There is no (37, 154, 738)-net in base 8, because

1 times m-reduction [i] would yield (37, 153, 738)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 585489 075910 502303 496958 649216 651854 797673 635264 398546 181964 238812 958136 328796 186308 307361 056565 754940 686354 919931 621121 839800 892562 133472 > 8¹⁵³ [i]