MinT - Best Known (99, 99+38, s)-Nets in Base 5

Best Known (99, 99+38, s)-Nets in Base 5

(99, 99+38, 408)-Net over F₅ — Constructive and digital

Digital (99, 137, 408)-net over F₅, using

1 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+38, 1437)-Net over F₅ — Digital

Digital (99, 137, 1437)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+38, 217304)-Net in Base 5 — Upper bound on s

There is no (99, 137, 217305)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 573973 670227 514512 096570 078807 045576 810935 444189 453068 972177 388864 938527 319126 486930 227732 664605 > 5¹³⁷ [i]