MinT - Best Known (142−68, 142, s)-Nets in Base 5

Best Known (142−68, 142, s)-Nets in Base 5

(142−68, 142, 104)-Net over F₅ — Constructive and digital

Digital (74, 142, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 71, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(142−68, 142, 161)-Net over F₅ — Digital

Digital (74, 142, 161)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−68, 142, 2784)-Net in Base 5 — Upper bound on s

There is no (74, 142, 2785)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1800 835217 221795 008278 711924 351128 434479 294579 409407 393351 287632 987375 823061 571843 912652 968442 199961 > 5¹⁴² [i]