MinT - Best Known (219−64, 219, s)-Nets in Base 3

Best Known (219−64, 219, s)-Nets in Base 3

(219−64, 219, 264)-Net over F₃ — Constructive and digital

Digital (155, 219, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 73, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(219−64, 219, 522)-Net over F₃ — Digital

Digital (155, 219, 522)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−64, 219, 11748)-Net in Base 3 — Upper bound on s

There is no (155, 219, 11749)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 309 019447 820916 926081 309060 463179 937967 289293 426460 320213 429082 237533 513643 113550 010441 591998 938630 150017 > 3²¹⁹ [i]