MinT - Best Known (161, 161+74, s)-Nets in Base 3

Best Known (161, 161+74, s)-Nets in Base 3

(161, 161+74, 192)-Net over F₃ — Constructive and digital

Digital (161, 235, 192)-net over F₃, using

3¹ times duplication [i] based on digital (160, 234, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 78, 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]

(161, 161+74, 438)-Net over F₃ — Digital

Digital (161, 235, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+74, 7820)-Net in Base 3 — Upper bound on s

There is no (161, 235, 7821)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13327 568681 934610 512658 422205 078977 024654 703081 498233 972614 122910 236696 487037 488500 911198 585044 202148 991860 348843 > 3²³⁵ [i]