MinT - Best Known (83, 83+67, s)-Nets in Base 3

Best Known (83, 83+67, s)-Nets in Base 3

(83, 83+67, 80)-Net over F₃ — Constructive and digital

Digital (83, 150, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 75, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(83, 83+67, 108)-Net over F₃ — Digital

Digital (83, 150, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+67, 906)-Net in Base 3 — Upper bound on s

There is no (83, 150, 907)-net in base 3, because

1 times m-reduction [i] would yield (83, 149, 907)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 124126 321427 524035 242163 654594 628441 690169 403952 291281 912406 447895 054295 > 3¹⁴⁹ [i]