MinT - Best Known (109, 109+44, s)-Nets in Base 3

Best Known (109, 109+44, s)-Nets in Base 3

(109, 109+44, 246)-Net over F₃ — Constructive and digital

Digital (109, 153, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 51, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(109, 109+44, 407)-Net over F₃ — Digital

Digital (109, 153, 407)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+44, 9397)-Net in Base 3 — Upper bound on s

There is no (109, 153, 9398)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 011178 964902 241173 702860 113585 939358 517434 727135 605648 548142 461726 589717 > 3¹⁵³ [i]