MinT - Best Known (93, 93+49, s)-Nets in Base 3

Best Known (93, 93+49, s)-Nets in Base 3

(93, 93+49, 156)-Net over F₃ — Constructive and digital

Digital (93, 142, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 71, 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]

(93, 93+49, 215)-Net over F₃ — Digital

Digital (93, 142, 215)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+49, 3091)-Net in Base 3 — Upper bound on s

There is no (93, 142, 3092)-net in base 3, because

1 times m-reduction [i] would yield (93, 141, 3092)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 898762 948762 429702 498264 142986 197461 151232 921485 493686 419737 878081 > 3¹⁴¹ [i]