MinT - Best Known (42−20, 42, s)-Nets in Base 9

Best Known (42−20, 42, s)-Nets in Base 9

(42−20, 42, 200)-Net over F₉ — Constructive and digital

Digital (22, 42, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 21, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(42−20, 42, 5757)-Net in Base 9 — Upper bound on s

There is no (22, 42, 5758)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11972 554516 542797 649330 484769 125018 591905 > 9⁴² [i]