MinT - Best Known (131−58, 131, s)-Nets in Base 9

Best Known (131−58, 131, s)-Nets in Base 9

(131−58, 131, 344)-Net over F₉ — Constructive and digital

Digital (73, 131, 344)-net over F₉, using

1 times m-reduction [i] based on digital (73, 132, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 66, 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]

(131−58, 131, 419)-Net over F₉ — Digital

Digital (73, 131, 419)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−58, 131, 29807)-Net in Base 9 — Upper bound on s

There is no (73, 131, 29808)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101430 026739 899135 162646 753245 295526 721340 524926 741143 697166 402712 527278 559163 712378 191249 904435 172711 049578 472625 495467 325825 > 9¹³¹ [i]