MinT - Best Known (94, 94+50, s)-Nets in Base 3

Best Known (94, 94+50, s)-Nets in Base 3

(94, 94+50, 156)-Net over F₃ — Constructive and digital

Digital (94, 144, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 72, 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]

(94, 94+50, 213)-Net over F₃ — Digital

Digital (94, 144, 213)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+50, 2825)-Net in Base 3 — Upper bound on s

There is no (94, 144, 2826)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 510 265893 163618 016480 361814 050876 922143 411727 494423 994535 217655 033509 > 3¹⁴⁴ [i]