MinT - Best Known (102, 102+45, s)-Nets in Base 3

Best Known (102, 102+45, s)-Nets in Base 3

(102, 102+45, 192)-Net over F₃ — Constructive and digital

Digital (102, 147, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 49, 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]

(102, 102+45, 320)-Net over F₃ — Digital

Digital (102, 147, 320)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+45, 6618)-Net in Base 3 — Upper bound on s

There is no (102, 147, 6619)-net in base 3, because

1 times m-reduction [i] would yield (102, 146, 6619)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4573 710487 279908 003252 343144 811038 379668 449957 285714 400695 654035 288301 > 3¹⁴⁶ [i]