MinT - Best Known (126−87, 126, s)-Nets in Base 8

Best Known (126−87, 126, s)-Nets in Base 8

(126−87, 126, 98)-Net over F₈ — Constructive and digital

Digital (39, 126, 98)-net over F₈, using

t-expansion [i] based on digital (37, 126, 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]

(126−87, 126, 129)-Net over F₈ — Digital

Digital (39, 126, 129)-net over F₈, using

t-expansion [i] based on digital (38, 126, 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]

(126−87, 126, 990)-Net in Base 8 — Upper bound on s

There is no (39, 126, 991)-net in base 8, because

1 times m-reduction [i] would yield (39, 125, 991)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 77596 898740 297700 527042 297575 901508 770825 199557 911096 669330 197913 161870 340819 938028 680463 269635 289204 488235 801560 > 8¹²⁵ [i]