MinT - Best Known (115, 115+50, s)-Nets in Base 3

Best Known (115, 115+50, s)-Nets in Base 3

(115, 115+50, 204)-Net over F₃ — Constructive and digital

Digital (115, 165, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 55, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(115, 115+50, 364)-Net over F₃ — Digital

Digital (115, 165, 364)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+50, 7146)-Net in Base 3 — Upper bound on s

There is no (115, 165, 7147)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312529 985225 729975 871320 431622 612396 085701 408625 760035 149316 740891 322302 505703 > 3¹⁶⁵ [i]