MinT - Best Known (149−44, 149, s)-Nets in Base 5

Best Known (149−44, 149, s)-Nets in Base 5

(149−44, 149, 408)-Net over F₅ — Constructive and digital

Digital (105, 149, 408)-net over F₅, using

1 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(149−44, 149, 1137)-Net over F₅ — Digital

Digital (105, 149, 1137)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−44, 149, 122650)-Net in Base 5 — Upper bound on s

There is no (105, 149, 122651)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 140456 669558 450975 080730 600211 710311 099924 984000 377972 261478 213054 127773 487875 056583 101829 218448 064425 > 5¹⁴⁹ [i]