MinT - Best Known (102, 102+39, s)-Nets in Base 3

Best Known (102, 102+39, s)-Nets in Base 3

(102, 102+39, 252)-Net over F₃ — Constructive and digital

Digital (102, 141, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 47, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(102, 102+39, 438)-Net over F₃ — Digital

Digital (102, 141, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+39, 12977)-Net in Base 3 — Upper bound on s

There is no (102, 141, 12978)-net in base 3, because

1 times m-reduction [i] would yield (102, 140, 12978)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 268593 603056 230165 521664 619288 020900 342813 546113 456289 280530 587633 > 3¹⁴⁰ [i]