MinT - Best Known (202−60, 202, s)-Nets in Base 3

Best Known (202−60, 202, s)-Nets in Base 3

(202−60, 202, 246)-Net over F₃ — Constructive and digital

Digital (142, 202, 246)-net over F₃, using

3¹ times duplication [i] based on digital (141, 201, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 67, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(202−60, 202, 461)-Net over F₃ — Digital

Digital (142, 202, 461)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−60, 202, 9796)-Net in Base 3 — Upper bound on s

There is no (142, 202, 9797)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 394178 671821 297403 402310 814535 896881 050707 137847 319430 011657 114481 918445 138497 967623 628195 555105 > 3²⁰² [i]