MinT - Best Known (221−75, 221, s)-Nets in Base 3

Best Known (221−75, 221, s)-Nets in Base 3

(221−75, 221, 162)-Net over F₃ — Constructive and digital

Digital (146, 221, 162)-net over F₃, using

7 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]

(221−75, 221, 328)-Net over F₃ — Digital

Digital (146, 221, 328)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−75, 221, 4996)-Net in Base 3 — Upper bound on s

There is no (146, 221, 4997)-net in base 3, because

1 times m-reduction [i] would yield (146, 220, 4997)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 929 424601 370128 089768 573912 418933 599217 704887 745220 088289 650317 457242 244603 196180 424483 221752 903744 602011 > 3²²⁰ [i]