MinT - Best Known (143−87, 143, s)-Nets in Base 8

Best Known (143−87, 143, s)-Nets in Base 8

(143−87, 143, 98)-Net over F₈ — Constructive and digital

Digital (56, 143, 98)-net over F₈, using

t-expansion [i] based on digital (37, 143, 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]

(143−87, 143, 144)-Net over F₈ — Digital

Digital (56, 143, 144)-net over F₈, using

t-expansion [i] based on digital (45, 143, 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]

(143−87, 143, 2288)-Net in Base 8 — Upper bound on s

There is no (56, 143, 2289)-net in base 8, because

1 times m-reduction [i] would yield (56, 142, 2289)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 174 663163 496103 867648 031754 024808 245191 708969 198409 069308 748689 378961 473340 293035 659652 582287 750790 075182 155640 177777 584220 476400 > 8¹⁴² [i]