MinT - Best Known (126−41, 126, s)-Nets in Base 5

Best Known (126−41, 126, s)-Nets in Base 5

(126−41, 126, 296)-Net over F₅ — Constructive and digital

Digital (85, 126, 296)-net over F₅, using

6 times m-reduction [i] based on digital (85, 132, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 66, 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]

(126−41, 126, 644)-Net over F₅ — Digital

Digital (85, 126, 644)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−41, 126, 48492)-Net in Base 5 — Upper bound on s

There is no (85, 126, 48493)-net in base 5, because

1 times m-reduction [i] would yield (85, 125, 48493)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2351 000796 087620 849758 974475 405784 137692 374116 544351 375023 242660 529146 998642 660641 654705 > 5¹²⁵ [i]