MinT - Best Known (82, 114, s)-Nets in Base 5

Best Known (82, 114, s)-Nets in Base 5

(82, 114, 400)-Net over F₅ — Constructive and digital

Digital (82, 114, 400)-net over F₅, using

trace code for nets [i] based on digital (25, 57, 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]

(82, 114, 1170)-Net over F₅ — Digital

Digital (82, 114, 1170)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 114, 162408)-Net in Base 5 — Upper bound on s

There is no (82, 114, 162409)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 149717 610468 005056 746497 400279 696330 356593 009550 589497 055993 938578 510351 950785 > 5¹¹⁴ [i]