MinT - Best Known (99, 99+35, s)-Nets in Base 5

Best Known (99, 99+35, s)-Nets in Base 5

(99, 99+35, 408)-Net over F₅ — Constructive and digital

Digital (99, 134, 408)-net over F₅, using

4 times m-reduction [i] based on digital (99, 138, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 69, 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]

(99, 99+35, 1941)-Net over F₅ — Digital

Digital (99, 134, 1941)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+35, 527579)-Net in Base 5 — Upper bound on s

There is no (99, 134, 527580)-net in base 5, because

1 times m-reduction [i] would yield (99, 133, 527580)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 383900 631021 808305 311967 431636 002661 745242 513582 562334 870329 842735 922615 770466 677548 620145 > 5¹³³ [i]