MinT - Best Known (42−22, 42, s)-Nets in Base 9

Best Known (42−22, 42, s)-Nets in Base 9

(42−22, 42, 74)-Net over F₉ — Constructive and digital

Digital (20, 42, 74)-net over F₉, using

t-expansion [i] based on digital (17, 42, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(42−22, 42, 76)-Net in Base 9 — Constructive

(20, 42, 76)-net in base 9, using

base change [i] based on digital (6, 28, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(42−22, 42, 86)-Net over F₉ — Digital

Digital (20, 42, 86)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(42−22, 42, 2693)-Net in Base 9 — Upper bound on s

There is no (20, 42, 2694)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11980 933794 843241 459809 068069 518138 482385 > 9⁴² [i]