MinT - Best Known (102, 102+41, s)-Nets in Base 3

Best Known (102, 102+41, s)-Nets in Base 3

(102, 102+41, 228)-Net over F₃ — Constructive and digital

Digital (102, 143, 228)-net over F₃, using

1 times m-reduction [i] based on digital (102, 144, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 48, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(102, 102+41, 390)-Net over F₃ — Digital

Digital (102, 143, 390)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+41, 10115)-Net in Base 3 — Upper bound on s

There is no (102, 143, 10116)-net in base 3, because

1 times m-reduction [i] would yield (102, 142, 10116)-net in base 3, but
- 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]