MinT - Best Known (38, 38+59, s)-Nets in Base 8

Best Known (38, 38+59, s)-Nets in Base 8

(38, 38+59, 98)-Net over F₈ — Constructive and digital

Digital (38, 97, 98)-net over F₈, using

t-expansion [i] based on digital (37, 97, 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]

(38, 38+59, 129)-Net over F₈ — Digital

Digital (38, 97, 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]

(38, 38+59, 1609)-Net in Base 8 — Upper bound on s

There is no (38, 97, 1610)-net in base 8, because

1 times m-reduction [i] would yield (38, 96, 1610)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 501 081128 752151 031044 221091 932733 998994 265963 921491 666143 961832 905943 292600 839242 774096 > 8⁹⁶ [i]