MinT - Best Known (45, 45+110, s)-Nets in Base 8

Best Known (45, 45+110, s)-Nets in Base 8

(45, 45+110, 98)-Net over F₈ — Constructive and digital

Digital (45, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(45, 45+110, 144)-Net over F₈ — Digital

Digital (45, 155, 144)-net over F₈, using

net from sequence [i] based on digital (45, 143)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(45, 45+110, 1034)-Net in Base 8 — Upper bound on s

There is no (45, 155, 1035)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 949277 148415 099417 120672 134089 412063 225024 207121 396998 486291 666930 336569 778565 884413 237369 276931 626375 370588 868849 004630 363503 532165 987840 > 8¹⁵⁵ [i]