MinT - Best Known (52, 52+46, s)-Nets in Base 5

Best Known (52, 52+46, s)-Nets in Base 5

(52, 52+46, 104)-Net over F₅ — Constructive and digital

Digital (52, 98, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 49, 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]

(52, 52+46, 127)-Net over F₅ — Digital

Digital (52, 98, 127)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+46, 2225)-Net in Base 5 — Upper bound on s

There is no (52, 98, 2226)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 318 159798 160093 078681 241599 037230 040994 690911 935503 152527 911776 072425 > 5⁹⁸ [i]