MinT - Best Known (87, 87+48, s)-Nets in Base 9

Best Known (87, 87+48, s)-Nets in Base 9

(87, 87+48, 740)-Net over F₉ — Constructive and digital

Digital (87, 135, 740)-net over F₉, using

7 times m-reduction [i] based on digital (87, 142, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 71, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(87, 87+48, 1288)-Net over F₉ — Digital

Digital (87, 135, 1288)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+48, 285670)-Net in Base 9 — Upper bound on s

There is no (87, 135, 285671)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 664 922100 663507 557436 037932 594762 520590 355026 797454 016989 592077 018757 002416 619135 414794 567128 989976 281178 088649 284277 983960 648001 > 9¹³⁵ [i]