MinT - Best Known (102, 102+43, s)-Nets in Base 3

Best Known (102, 102+43, s)-Nets in Base 3

(102, 102+43, 204)-Net over F₃ — Constructive and digital

Digital (102, 145, 204)-net over F₃, using

3¹ times duplication [i] based on digital (101, 144, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 48, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(102, 102+43, 351)-Net over F₃ — Digital

Digital (102, 145, 351)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+43, 8091)-Net in Base 3 — Upper bound on s

There is no (102, 145, 8092)-net in base 3, because

1 times m-reduction [i] would yield (102, 144, 8092)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 507 587093 379800 825420 129959 101887 631344 282748 407292 177727 847215 339545 > 3¹⁴⁴ [i]