MinT - Best Known (170−131, 170, s)-Nets in Base 8

Best Known (170−131, 170, s)-Nets in Base 8

(170−131, 170, 98)-Net over F₈ — Constructive and digital

Digital (39, 170, 98)-net over F₈, using

t-expansion [i] based on 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]

(170−131, 170, 129)-Net over F₈ — Digital

Digital (39, 170, 129)-net over F₈, using

t-expansion [i] based on digital (38, 170, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(170−131, 170, 756)-Net in Base 8 — Upper bound on s

There is no (39, 170, 757)-net in base 8, because

1 times m-reduction [i] would yield (39, 169, 757)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 429 492934 829782 736155 098553 830041 591981 195693 596257 840071 403291 024956 562577 920282 461498 728359 937337 634529 729653 038721 380514 344915 434923 642473 722326 977284 > 8¹⁶⁹ [i]