MinT - Best Known (181−62, 181, s)-Nets in Base 3

Best Known (181−62, 181, s)-Nets in Base 3

(181−62, 181, 156)-Net over F₃ — Constructive and digital

Digital (119, 181, 156)-net over F₃, using

13 times m-reduction [i] based on digital (119, 194, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 97, 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]

(181−62, 181, 269)-Net over F₃ — Digital

Digital (119, 181, 269)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−62, 181, 3760)-Net in Base 3 — Upper bound on s

There is no (119, 181, 3761)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 922524 686664 654490 812018 460811 085735 571591 901102 526370 692045 229389 625807 531030 545643 > 3¹⁸¹ [i]