MinT - Best Known (170−133, 170, s)-Nets in Base 8

Best Known (170−133, 170, s)-Nets in Base 8

(170−133, 170, 98)-Net over F₈ — Constructive and digital

Digital (37, 170, 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]

(170−133, 170, 121)-Net over F₈ — Digital

Digital (37, 170, 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]

(170−133, 170, 704)-Net in Base 8 — Upper bound on s

There is no (37, 170, 705)-net in base 8, because

1 times m-reduction [i] would yield (37, 169, 705)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 446 984142 004246 284137 198959 618569 533910 656098 957489 823087 795448 717266 794052 241454 387269 386576 927621 436181 428722 678960 306936 353743 429333 517367 221671 103744 > 8¹⁶⁹ [i]