MinT - Best Known (84−24, 84, s)-Nets in Base 3

Best Known (84−24, 84, s)-Nets in Base 3

(84−24, 84, 192)-Net over F₃ — Constructive and digital

Digital (60, 84, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 28, 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]

(84−24, 84, 268)-Net over F₃ — Digital

Digital (60, 84, 268)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−24, 84, 5771)-Net in Base 3 — Upper bound on s

There is no (60, 84, 5772)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11975 764055 321215 207450 799027 802305 608641 > 3⁸⁴ [i]