MinT - Best Known (54, 54+48, s)-Nets in Base 5

Best Known (54, 54+48, s)-Nets in Base 5

(54, 54+48, 104)-Net over F₅ — Constructive and digital

Digital (54, 102, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 51, 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]

(54, 54+48, 130)-Net over F₅ — Digital

Digital (54, 102, 130)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+48, 2273)-Net in Base 5 — Upper bound on s

There is no (54, 102, 2274)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 199247 484833 435295 613630 964473 773312 224635 798560 810887 491189 016510 629505 > 5¹⁰² [i]