MinT - Best Known (128−33, 128, s)-Nets in Base 5

Best Known (128−33, 128, s)-Nets in Base 5

(128−33, 128, 408)-Net over F₅ — Constructive and digital

Digital (95, 128, 408)-net over F₅, using

2 times m-reduction [i] based on digital (95, 130, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 65, 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]

(128−33, 128, 2014)-Net over F₅ — Digital

Digital (95, 128, 2014)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−33, 128, 600543)-Net in Base 5 — Upper bound on s

There is no (95, 128, 600544)-net in base 5, because

1 times m-reduction [i] would yield (95, 127, 600544)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58774 730352 150405 591694 066862 660685 843821 023474 136465 438219 740993 818403 916211 781560 246273 > 5¹²⁷ [i]