MinT - Best Known (173, 173+75, s)-Nets in Base 3

Best Known (173, 173+75, s)-Nets in Base 3

(173, 173+75, 246)-Net over F₃ — Constructive and digital

Digital (173, 248, 246)-net over F₃, using

1 times m-reduction [i] based on digital (173, 249, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 83, 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]

(173, 173+75, 522)-Net over F₃ — Digital

Digital (173, 248, 522)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+75, 11183)-Net in Base 3 — Upper bound on s

There is no (173, 248, 11184)-net in base 3, because

1 times m-reduction [i] would yield (173, 247, 11184)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7075 446367 393854 685167 381237 921148 596463 500216 003483 709881 449271 643940 991543 984530 195146 868773 766270 949011 886234 889569 > 3²⁴⁷ [i]