MinT - Best Known (137−97, 137, s)-Nets in Base 8

Best Known (137−97, 137, s)-Nets in Base 8

(137−97, 137, 98)-Net over F₈ — Constructive and digital

Digital (40, 137, 98)-net over F₈, using

t-expansion [i] based on digital (37, 137, 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]

(137−97, 137, 129)-Net over F₈ — Digital

Digital (40, 137, 129)-net over F₈, using

t-expansion [i] based on digital (38, 137, 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]

(137−97, 137, 939)-Net in Base 8 — Upper bound on s

There is no (40, 137, 940)-net in base 8, because

1 times m-reduction [i] would yield (40, 136, 940)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 687 686510 002982 681511 613748 035232 318955 940892 611490 858111 299813 010710 569929 712329 267438 896398 690861 871681 247758 207393 812648 > 8¹³⁶ [i]