MinT - Best Known (217−71, 217, s)-Nets in Base 3

Best Known (217−71, 217, s)-Nets in Base 3

(217−71, 217, 162)-Net over F₃ — Constructive and digital

Digital (146, 217, 162)-net over F₃, using

11 times m-reduction [i] based on digital (146, 228, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 114, 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]

(217−71, 217, 362)-Net over F₃ — Digital

Digital (146, 217, 362)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−71, 217, 6085)-Net in Base 3 — Upper bound on s

There is no (146, 217, 6086)-net in base 3, because

1 times m-reduction [i] would yield (146, 216, 6086)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 459288 521614 609157 245055 417405 654019 941040 899088 087904 397382 073517 841335 813686 335816 714937 911645 205153 > 3²¹⁶ [i]