MinT - Best Known (229−81, 229, s)-Nets in Base 3

Best Known (229−81, 229, s)-Nets in Base 3

(229−81, 229, 162)-Net over F₃ — Constructive and digital

Digital (148, 229, 162)-net over F₃, using

3 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]

(229−81, 229, 299)-Net over F₃ — Digital

Digital (148, 229, 299)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−81, 229, 4094)-Net in Base 3 — Upper bound on s

There is no (148, 229, 4095)-net in base 3, because

1 times m-reduction [i] would yield (148, 228, 4095)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 106831 962623 363416 450849 412311 332667 603278 661563 849907 925253 804463 261397 361312 012723 954256 312214 717298 704305 > 3²²⁸ [i]