MinT - Best Known (79, 79+35, s)-Nets in Base 3

Best Known (79, 79+35, s)-Nets in Base 3

(79, 79+35, 156)-Net over F₃ — Constructive and digital

Digital (79, 114, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 57, 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]

(79, 79+35, 258)-Net over F₃ — Digital

Digital (79, 114, 258)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+35, 5309)-Net in Base 3 — Upper bound on s

There is no (79, 114, 5310)-net in base 3, because

1 times m-reduction [i] would yield (79, 113, 5310)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 823995 097968 725262 074709 763081 427851 394336 902586 194781 > 3¹¹³ [i]