MinT - Best Known (135−35, 135, s)-Nets in Base 5

Best Known (135−35, 135, s)-Nets in Base 5

(135−35, 135, 408)-Net over F₅ — Constructive and digital

Digital (100, 135, 408)-net over F₅, using

5 times m-reduction [i] based on digital (100, 140, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 70, 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]

(135−35, 135, 2034)-Net over F₅ — Digital

Digital (100, 135, 2034)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−35, 135, 579968)-Net in Base 5 — Upper bound on s

There is no (100, 135, 579969)-net in base 5, because

1 times m-reduction [i] would yield (100, 134, 579969)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4591 859044 840292 722426 356903 211832 083662 618593 042025 394863 404608 856614 307180 008138 524611 712197 > 5¹³⁴ [i]