MinT - Best Known (149−45, 149, s)-Nets in Base 5

Best Known (149−45, 149, s)-Nets in Base 5

(149−45, 149, 400)-Net over F₅ — Constructive and digital

Digital (104, 149, 400)-net over F₅, using

t-expansion [i] based on digital (100, 149, 400)-net over F₅, using
- 1 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
  - trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(149−45, 149, 1026)-Net over F₅ — Digital

Digital (104, 149, 1026)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−45, 149, 113997)-Net in Base 5 — Upper bound on s

There is no (104, 149, 113998)-net in base 5, because

1 times m-reduction [i] would yield (104, 148, 113998)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 030649 653263 965917 863863 666689 207425 469726 939904 936449 831451 073677 514738 162752 599887 488545 893946 339521 > 5¹⁴⁸ [i]