MinT - Best Known (98−52, 98, s)-Nets in Base 8

Best Known (98−52, 98, s)-Nets in Base 8

(98−52, 98, 98)-Net over F₈ — Constructive and digital

Digital (46, 98, 98)-net over F₈, using

t-expansion [i] based on digital (37, 98, 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]

(98−52, 98, 144)-Net over F₈ — Digital

Digital (46, 98, 144)-net over F₈, using

t-expansion [i] based on digital (45, 98, 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]

(98−52, 98, 3804)-Net in Base 8 — Upper bound on s

There is no (46, 98, 3805)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31922 989197 455296 344855 331295 362491 727824 145143 905911 008963 456955 296552 838847 465580 573202 > 8⁹⁸ [i]