MinT - Best Known (124−53, 124, s)-Nets in Base 5

Best Known (124−53, 124, s)-Nets in Base 5

(124−53, 124, 208)-Net over F₅ — Constructive and digital

Digital (71, 124, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 62, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(124−53, 124, 215)-Net over F₅ — Digital

Digital (71, 124, 215)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−53, 124, 5325)-Net in Base 5 — Upper bound on s

There is no (71, 124, 5326)-net in base 5, because

1 times m-reduction [i] would yield (71, 123, 5326)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 303981 185325 973511 186621 387827 972644 780350 350222 415074 323359 275031 247595 717081 683585 > 5¹²³ [i]