MinT - Best Known (226−78, 226, s)-Nets in Base 3

Best Known (226−78, 226, s)-Nets in Base 3

(226−78, 226, 162)-Net over F₃ — Constructive and digital

Digital (148, 226, 162)-net over F₃, using

6 times m-reduction [i] based on digital (148, 232, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 116, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(226−78, 226, 318)-Net over F₃ — Digital

Digital (148, 226, 318)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−78, 226, 4441)-Net in Base 3 — Upper bound on s

There is no (148, 226, 4442)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 678887 394190 034478 600916 769994 373463 836192 246344 360404 157090 923108 433364 014979 684800 768862 104883 658995 651273 > 3²²⁶ [i]