MinT - Best Known (84, 120, s)-Nets in Base 3

Best Known (84, 120, s)-Nets in Base 3

(84, 120, 192)-Net over F₃ — Constructive and digital

Digital (84, 120, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 40, 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]

(84, 120, 291)-Net over F₃ — Digital

Digital (84, 120, 291)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 120, 5709)-Net in Base 3 — Upper bound on s

There is no (84, 120, 5710)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1801 109685 153394 929150 467305 239327 074168 204296 220818 276221 > 3¹²⁰ [i]