MinT - Best Known (108, 108+43, s)-Nets in Base 3

Best Known (108, 108+43, s)-Nets in Base 3

(108, 108+43, 246)-Net over F₃ — Constructive and digital

Digital (108, 151, 246)-net over F₃, using

3¹ times duplication [i] based on digital (107, 150, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 50, 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]

(108, 108+43, 417)-Net over F₃ — Digital

Digital (108, 151, 417)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+43, 11083)-Net in Base 3 — Upper bound on s

There is no (108, 151, 11084)-net in base 3, because

1 times m-reduction [i] would yield (108, 150, 11084)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370469 264275 726481 429978 959339 871130 910599 376266 682472 171230 878381 082233 > 3¹⁵⁰ [i]