MinT - Best Known (70, 70+27, s)-Nets in Base 5

Best Known (70, 70+27, s)-Nets in Base 5

(70, 70+27, 296)-Net over F₅ — Constructive and digital

Digital (70, 97, 296)-net over F₅, using

5 times m-reduction [i] based on digital (70, 102, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 51, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+27, 1082)-Net over F₅ — Digital

Digital (70, 97, 1082)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+27, 205566)-Net in Base 5 — Upper bound on s

There is no (70, 97, 205567)-net in base 5, because

1 times m-reduction [i] would yield (70, 96, 205567)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 622569 836330 551200 899247 584858 284359 256892 200146 322770 103652 207565 > 5⁹⁶ [i]