MinT - Best Known (73, 73+35, s)-Nets in Base 5

Best Known (73, 73+35, s)-Nets in Base 5

(73, 73+35, 296)-Net over F₅ — Constructive and digital

Digital (73, 108, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 54, 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]

(73, 73+35, 579)-Net over F₅ — Digital

Digital (73, 108, 579)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+35, 44995)-Net in Base 5 — Upper bound on s

There is no (73, 108, 44996)-net in base 5, because

1 times m-reduction [i] would yield (73, 107, 44996)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 616 477598 782567 624692 180656 500413 953733 505800 705504 537273 217829 139356 147985 > 5¹⁰⁷ [i]