MinT - Best Known (80−37, 80, s)-Nets in Base 5

Best Known (80−37, 80, s)-Nets in Base 5

(80−37, 80, 104)-Net over F₅ — Constructive and digital

Digital (43, 80, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 40, 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]

(80−37, 80, 115)-Net over F₅ — Digital

Digital (43, 80, 115)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−37, 80, 2193)-Net in Base 5 — Upper bound on s

There is no (43, 80, 2194)-net in base 5, because

1 times m-reduction [i] would yield (43, 79, 2194)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 16 560855 237934 029362 122620 749124 011368 319763 491795 035201 > 5⁷⁹ [i]