MinT - Best Known (110−34, 110, s)-Nets in Base 5

Best Known (110−34, 110, s)-Nets in Base 5

(110−34, 110, 296)-Net over F₅ — Constructive and digital

Digital (76, 110, 296)-net over F₅, using

4 times m-reduction [i] based on digital (76, 114, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 57, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(110−34, 110, 720)-Net over F₅ — Digital

Digital (76, 110, 720)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−34, 110, 59778)-Net in Base 5 — Upper bound on s

There is no (76, 110, 59779)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77053 254060 379220 594275 417805 382648 018014 247073 633786 037409 686532 014044 176845 > 5¹¹⁰ [i]