MinT - Best Known (64, 64+58, s)-Nets in Base 5

Best Known (64, 64+58, s)-Nets in Base 5

(64, 64+58, 104)-Net over F₅ — Constructive and digital

Digital (64, 122, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 61, 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]

(64, 64+58, 145)-Net over F₅ — Digital

Digital (64, 122, 145)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+58, 2523)-Net in Base 5 — Upper bound on s

There is no (64, 122, 2524)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 19 013866 889117 204664 880409 631349 581164 414466 740794 368465 326331 427343 202819 137978 704625 > 5¹²² [i]