MinT - Best Known (178, 178+58, s)-Nets in Base 3

Best Known (178, 178+58, s)-Nets in Base 3

(178, 178+58, 400)-Net over F₃ — Constructive and digital

Digital (178, 236, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 59, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(178, 178+58, 1042)-Net over F₃ — Digital

Digital (178, 236, 1042)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+58, 44523)-Net in Base 3 — Upper bound on s

There is no (178, 236, 44524)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39867 516988 355912 166110 819664 967059 079804 815397 596793 566261 798557 442122 161428 260174 367031 247480 781627 218395 109049 > 3²³⁶ [i]