MinT - Best Known (73, 73+59, s)-Nets in Base 5

Best Known (73, 73+59, s)-Nets in Base 5

(73, 73+59, 132)-Net over F₅ — Constructive and digital

Digital (73, 132, 132)-net over F₅, using

6 times m-reduction [i] based on digital (73, 138, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 69, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(73, 73+59, 192)-Net over F₅ — Digital

Digital (73, 132, 192)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+59, 4171)-Net in Base 5 — Upper bound on s

There is no (73, 132, 4172)-net in base 5, because

1 times m-reduction [i] would yield (73, 131, 4172)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 902618 586875 924704 936414 218761 145377 026263 827586 794031 748079 491322 254012 372576 054601 215665 > 5¹³¹ [i]