MinT - Best Known (133−43, 133, s)-Nets in Base 5

Best Known (133−43, 133, s)-Nets in Base 5

(133−43, 133, 296)-Net over F₅ — Constructive and digital

Digital (90, 133, 296)-net over F₅, using

9 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(133−43, 133, 692)-Net over F₅ — Digital

Digital (90, 133, 692)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−43, 133, 53682)-Net in Base 5 — Upper bound on s

There is no (90, 133, 53683)-net in base 5, because

1 times m-reduction [i] would yield (90, 132, 53683)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 687000 696218 973517 847883 044582 870396 634673 621499 933056 723513 341161 835139 808232 780627 991165 > 5¹³² [i]