MinT - Best Known (159−114, 159, s)-Nets in Base 8

Best Known (159−114, 159, s)-Nets in Base 8

(159−114, 159, 98)-Net over F₈ — Constructive and digital

Digital (45, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(159−114, 159, 144)-Net over F₈ — Digital

Digital (45, 159, 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]

(159−114, 159, 1006)-Net in Base 8 — Upper bound on s

There is no (45, 159, 1007)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 397703 289545 960606 329289 391048 010366 520275 243701 884451 876203 007173 079579 180778 715806 360229 452965 458795 244119 897100 194658 946113 137999 280495 618920 > 8¹⁵⁹ [i]