MinT - Best Known (198−62, 198, s)-Nets in Base 3

Best Known (198−62, 198, s)-Nets in Base 3

(198−62, 198, 192)-Net over F₃ — Constructive and digital

Digital (136, 198, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 66, 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]

(198−62, 198, 384)-Net over F₃ — Digital

Digital (136, 198, 384)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−62, 198, 6894)-Net in Base 3 — Upper bound on s

There is no (136, 198, 6895)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29565 442744 834997 122344 680314 421351 647420 858121 214293 246293 936891 225498 624736 388045 158650 045827 > 3¹⁹⁸ [i]