MinT - Best Known (73, 105, s)-Nets in Base 3

Best Known (73, 105, s)-Nets in Base 3

(73, 105, 156)-Net over F₃ — Constructive and digital

Digital (73, 105, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 35, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(73, 105, 249)-Net over F₃ — Digital

Digital (73, 105, 249)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 105, 4583)-Net in Base 3 — Upper bound on s

There is no (73, 105, 4584)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 660075 461986 845642 150961 307922 080362 508904 987649 > 3¹⁰⁵ [i]