MinT - Best Known (114, 114+63, s)-Nets in Base 3

Best Known (114, 114+63, s)-Nets in Base 3

(114, 114+63, 156)-Net over F₃ — Constructive and digital

Digital (114, 177, 156)-net over F₃, using

7 times m-reduction [i] based on digital (114, 184, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 92, 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]

(114, 114+63, 235)-Net over F₃ — Digital

Digital (114, 177, 235)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+63, 3145)-Net in Base 3 — Upper bound on s

There is no (114, 177, 3146)-net in base 3, because

1 times m-reduction [i] would yield (114, 176, 3146)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 947996 688302 284066 108240 222782 102434 738256 094669 580244 473657 373664 005790 405852 363609 > 3¹⁷⁶ [i]