MinT - Best Known (222−70, 222, s)-Nets in Base 3

Best Known (222−70, 222, s)-Nets in Base 3

(222−70, 222, 192)-Net over F₃ — Constructive and digital

Digital (152, 222, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 74, 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]

(222−70, 222, 415)-Net over F₃ — Digital

Digital (152, 222, 415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−70, 222, 7353)-Net in Base 3 — Upper bound on s

There is no (152, 222, 7354)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8339 669259 924612 962669 982608 490473 789546 955917 039247 605436 886640 940851 757211 986965 807417 075118 419689 412529 > 3²²² [i]