MinT - Best Known (155, 155+67, s)-Nets in Base 3

Best Known (155, 155+67, s)-Nets in Base 3

(155, 155+67, 246)-Net over F₃ — Constructive and digital

Digital (155, 222, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 74, 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]

(155, 155+67, 476)-Net over F₃ — Digital

Digital (155, 222, 476)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+67, 10285)-Net in Base 3 — Upper bound on s

There is no (155, 222, 10286)-net in base 3, because

1 times m-reduction [i] would yield (155, 221, 10286)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2783 502594 731710 119388 498955 050293 377264 099627 493316 457578 635103 879653 944077 488322 715076 214658 650327 740445 > 3²²¹ [i]