MinT - Best Known (131−56, 131, s)-Nets in Base 9

Best Known (131−56, 131, s)-Nets in Base 9

(131−56, 131, 344)-Net over F₉ — Constructive and digital

Digital (75, 131, 344)-net over F₉, using

5 times m-reduction [i] based on digital (75, 136, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 68, 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]

(131−56, 131, 493)-Net over F₉ — Digital

Digital (75, 131, 493)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−56, 131, 41136)-Net in Base 9 — Upper bound on s

There is no (75, 131, 41137)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101371 456963 583140 132388 091916 864612 835485 963935 814529 429426 298026 902381 537857 477749 434090 134033 390720 933474 200647 627078 104417 > 9¹³¹ [i]