MinT - Best Known (102, 142, s)-Nets in Base 3

Best Known (102, 142, s)-Nets in Base 3

(102, 142, 246)-Net over F₃ — Constructive and digital

Digital (102, 142, 246)-net over F₃, using

3¹ times duplication [i] based on digital (101, 141, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 47, 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]

(102, 142, 412)-Net over F₃ — Digital

Digital (102, 142, 412)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 142, 10115)-Net in Base 3 — Upper bound on s

There is no (102, 142, 10116)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 411210 077905 024382 855542 346577 398205 594076 160417 993414 566177 188673 > 3¹⁴² [i]