MinT - Best Known (89, 156, s)-Nets in Base 3

Best Known (89, 156, s)-Nets in Base 3

(89, 156, 80)-Net over F₃ — Constructive and digital

Digital (89, 156, 80)-net over F₃, using

6 times m-reduction [i] based on digital (89, 162, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 81, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(89, 156, 124)-Net over F₃ — Digital

Digital (89, 156, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 156, 1114)-Net in Base 3 — Upper bound on s

There is no (89, 156, 1115)-net in base 3, because

1 times m-reduction [i] would yield (89, 155, 1115)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91 709175 881321 983047 822354 436778 565559 430445 807887 355539 527374 813185 954167 > 3¹⁵⁵ [i]