MinT - Best Known (106−50, 106, s)-Nets in Base 5

Best Known (106−50, 106, s)-Nets in Base 5

(106−50, 106, 104)-Net over F₅ — Constructive and digital

Digital (56, 106, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 53, 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]

(106−50, 106, 133)-Net over F₅ — Digital

Digital (56, 106, 133)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−50, 106, 2321)-Net in Base 5 — Upper bound on s

There is no (56, 106, 2322)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123 644258 480013 832658 446878 024849 992558 062488 196930 697343 590502 306755 516233 > 5¹⁰⁶ [i]