MinT - Best Known (143−103, 143, s)-Nets in Base 8

Best Known (143−103, 143, s)-Nets in Base 8

(143−103, 143, 98)-Net over F₈ — Constructive and digital

Digital (40, 143, 98)-net over F₈, using

t-expansion [i] based on digital (37, 143, 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]

(143−103, 143, 129)-Net over F₈ — Digital

Digital (40, 143, 129)-net over F₈, using

t-expansion [i] based on digital (38, 143, 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]

(143−103, 143, 895)-Net in Base 8 — Upper bound on s

There is no (40, 143, 896)-net in base 8, because

1 times m-reduction [i] would yield (40, 142, 896)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 179 101008 025257 713425 453147 319342 913610 959789 041329 712679 057662 391137 541759 667289 722926 869327 398255 954511 885196 213215 209952 142997 > 8¹⁴² [i]