MinT - Best Known (133−49, 133, s)-Nets in Base 5

Best Known (133−49, 133, s)-Nets in Base 5

(133−49, 133, 252)-Net over F₅ — Constructive and digital

Digital (84, 133, 252)-net over F₅, using

15 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(133−49, 133, 395)-Net over F₅ — Digital

Digital (84, 133, 395)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−49, 133, 17107)-Net in Base 5 — Upper bound on s

There is no (84, 133, 17108)-net in base 5, because

1 times m-reduction [i] would yield (84, 132, 17108)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 725081 874749 985872 710823 744712 489927 583388 485859 763820 494303 395341 820913 071019 666608 333825 > 5¹³² [i]