MinT - Best Known (85, 85+65, s)-Nets in Base 9

Best Known (85, 85+65, s)-Nets in Base 9

(85, 85+65, 344)-Net over F₉ — Constructive and digital

Digital (85, 150, 344)-net over F₉, using

t-expansion [i] based on digital (82, 150, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 75, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(85, 85+65, 518)-Net over F₉ — Digital

Digital (85, 150, 518)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+65, 44339)-Net in Base 9 — Upper bound on s

There is no (85, 150, 44340)-net in base 9, because

1 times m-reduction [i] would yield (85, 149, 44340)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15215 267702 958870 404491 960232 247899 876538 660907 298429 981978 279194 862942 620530 442524 952799 239987 263434 872944 701932 261783 734749 603499 346939 751425 > 9¹⁴⁹ [i]