MinT - Best Known (135−56, 135, s)-Nets in Base 9

Best Known (135−56, 135, s)-Nets in Base 9

(135−56, 135, 344)-Net over F₉ — Constructive and digital

Digital (79, 135, 344)-net over F₉, using

9 times m-reduction [i] based on digital (79, 144, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 72, 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]

(135−56, 135, 584)-Net over F₉ — Digital

Digital (79, 135, 584)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−56, 135, 56311)-Net in Base 9 — Upper bound on s

There is no (79, 135, 56312)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 665 082686 382762 799153 350488 071879 092525 942454 821429 557416 216358 674153 475253 504052 976523 856675 823658 713617 067955 842685 142977 392385 > 9¹³⁵ [i]