MinT - Best Known (83, 83+39, s)-Nets in Base 3

Best Known (83, 83+39, s)-Nets in Base 3

(83, 83+39, 156)-Net over F₃ — Constructive and digital

Digital (83, 122, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 61, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(83, 83+39, 240)-Net over F₃ — Digital

Digital (83, 122, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+39, 4313)-Net in Base 3 — Upper bound on s

There is no (83, 122, 4314)-net in base 3, because

1 times m-reduction [i] would yield (83, 121, 4314)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5400 641206 940110 542256 911793 478232 484132 489742 370500 221393 > 3¹²¹ [i]