MinT - Best Known (221−73, 221, s)-Nets in Base 3

Best Known (221−73, 221, s)-Nets in Base 3

(221−73, 221, 162)-Net over F₃ — Constructive and digital

Digital (148, 221, 162)-net over F₃, using

11 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]

(221−73, 221, 357)-Net over F₃ — Digital

Digital (148, 221, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−73, 221, 5845)-Net in Base 3 — Upper bound on s

There is no (148, 221, 5846)-net in base 3, because

1 times m-reduction [i] would yield (148, 220, 5846)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 928 708055 276555 790430 096348 188948 332896 782354 987339 141198 497435 381800 539897 036434 976284 874287 293064 155977 > 3²²⁰ [i]