MinT - Best Known (145−37, 145, s)-Nets in Base 5

Best Known (145−37, 145, s)-Nets in Base 5

(145−37, 145, 416)-Net over F₅ — Constructive and digital

Digital (108, 145, 416)-net over F₅, using

1 times m-reduction [i] based on digital (108, 146, 416)-net over F₅, using
- trace code for nets [i] based on digital (35, 73, 208)-net over F₂₅, using
  - net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
      - a function field by GarcÃa and Quoos [i]

(145−37, 145, 2351)-Net over F₅ — Digital

Digital (108, 145, 2351)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−37, 145, 737602)-Net in Base 5 — Upper bound on s

There is no (108, 145, 737603)-net in base 5, because

1 times m-reduction [i] would yield (108, 144, 737603)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44841 975641 076899 245257 722027 933065 672931 203840 377353 985497 592508 440029 852363 296590 825121 876135 136825 > 5¹⁴⁴ [i]