MinT - Best Known (129−85, 129, s)-Nets in Base 8

Best Known (129−85, 129, s)-Nets in Base 8

(129−85, 129, 98)-Net over F₈ — Constructive and digital

Digital (44, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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]

(129−85, 129, 130)-Net over F₈ — Digital

Digital (44, 129, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(129−85, 129, 1307)-Net in Base 8 — Upper bound on s

There is no (44, 129, 1308)-net in base 8, because

1 times m-reduction [i] would yield (44, 128, 1308)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 40 517755 712537 416747 960337 664035 623085 784435 730542 480801 223354 188672 441585 236241 008621 197277 922211 975746 551753 503944 > 8¹²⁸ [i]