MinT - Best Known (150−69, 150, s)-Nets in Base 9

Best Known (150−69, 150, s)-Nets in Base 9

(150−69, 150, 320)-Net over F₉ — Constructive and digital

Digital (81, 150, 320)-net over F₉, using

t-expansion [i] based on digital (80, 150, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 75, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(150−69, 150, 397)-Net over F₉ — Digital

Digital (81, 150, 397)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−69, 150, 25695)-Net in Base 9 — Upper bound on s

There is no (81, 150, 25696)-net in base 9, because

1 times m-reduction [i] would yield (81, 149, 25696)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15213 843348 549241 300539 349693 581762 690790 352944 985036 433896 237265 949599 607425 181371 702730 406852 090172 562819 618313 599265 971056 791018 280670 851585 > 9¹⁴⁹ [i]