MinT - Best Known (156−48, 156, s)-Nets in Base 3

Best Known (156−48, 156, s)-Nets in Base 3

(156−48, 156, 192)-Net over F₃ — Constructive and digital

Digital (108, 156, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 52, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(156−48, 156, 331)-Net over F₃ — Digital

Digital (108, 156, 331)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−48, 156, 6165)-Net in Base 3 — Upper bound on s

There is no (108, 156, 6166)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270 199869 769738 624160 270707 174586 658230 522708 880276 239986 092409 218850 558833 > 3¹⁵⁶ [i]