MinT - Best Known (100, 100+50, s)-Nets in Base 5

Best Known (100, 100+50, s)-Nets in Base 5

(100, 100+50, 400)-Net over F₅ — Constructive and digital

Digital (100, 150, 400)-net over F₅, using

trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(100, 100+50, 662)-Net over F₅ — Digital

Digital (100, 150, 662)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+50, 39736)-Net in Base 5 — Upper bound on s

There is no (100, 150, 39737)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 700 995940 968970 065008 595442 961291 235095 935534 718928 613893 289809 403740 802262 510648 588570 829125 306320 235781 > 5¹⁵⁰ [i]