MinT - Best Known (64, 64+56, s)-Nets in Base 5

Best Known (64, 64+56, s)-Nets in Base 5

(64, 64+56, 132)-Net over F₅ — Constructive and digital

Digital (64, 120, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 60, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(64, 64+56, 153)-Net over F₅ — Digital

Digital (64, 120, 153)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+56, 2775)-Net in Base 5 — Upper bound on s

There is no (64, 120, 2776)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 755997 626914 577072 731037 278167 916382 120982 073724 984458 121658 513384 509215 518413 466625 > 5¹²⁰ [i]