MinT - Best Known (61, 61+26, s)-Nets in Base 3

Best Known (61, 61+26, s)-Nets in Base 3

(61, 61+26, 156)-Net over F₃ — Constructive and digital

Digital (61, 87, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 29, 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]

(61, 61+26, 233)-Net over F₃ — Digital

Digital (61, 87, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+26, 4407)-Net in Base 3 — Upper bound on s

There is no (61, 87, 4408)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 323756 774250 490757 324404 348944 862010 637681 > 3⁸⁷ [i]