MinT - Best Known (113, 113+69, s)-Nets in Base 3

Best Known (113, 113+69, s)-Nets in Base 3

(113, 113+69, 156)-Net over F₃ — Constructive and digital

Digital (113, 182, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 91, 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]

(113, 113+69, 201)-Net over F₃ — Digital

Digital (113, 182, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+69, 2313)-Net in Base 3 — Upper bound on s

There is no (113, 182, 2314)-net in base 3, because

1 times m-reduction [i] would yield (113, 181, 2314)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 231 312596 035687 884401 126197 185959 819744 164917 792229 641237 215286 744860 806212 087666 352197 > 3¹⁸¹ [i]