MinT - Best Known (49, 49+74, s)-Nets in Base 8

Best Known (49, 49+74, s)-Nets in Base 8

(49, 49+74, 98)-Net over F₈ — Constructive and digital

Digital (49, 123, 98)-net over F₈, using

t-expansion [i] based on digital (37, 123, 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]

(49, 49+74, 144)-Net over F₈ — Digital

Digital (49, 123, 144)-net over F₈, using

t-expansion [i] based on digital (45, 123, 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]

(49, 49+74, 2080)-Net in Base 8 — Upper bound on s

There is no (49, 123, 2081)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1213 852941 712330 287650 937782 984768 019759 928904 685363 830908 273435 394481 985886 441666 850936 525450 732275 782432 475136 > 8¹²³ [i]