MinT - Best Known (107, 149, s)-Nets in Base 5

Best Known (107, 149, s)-Nets in Base 5

(107, 149, 408)-Net over F₅ — Constructive and digital

Digital (107, 149, 408)-net over F₅, using

t-expansion [i] based on 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]

(107, 149, 1420)-Net over F₅ — Digital

Digital (107, 149, 1420)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 149, 197586)-Net in Base 5 — Upper bound on s

There is no (107, 149, 197587)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 134632 718213 702857 349449 924446 789681 937460 370425 477935 265920 019263 791721 226336 183161 751887 681692 334845 > 5¹⁴⁹ [i]