MinT - Best Known (137, 202, s)-Nets in Base 3

Best Known (137, 202, s)-Nets in Base 3

(137, 202, 162)-Net over F₃ — Constructive and digital

Digital (137, 202, 162)-net over F₃, using

8 times m-reduction [i] based on digital (137, 210, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 105, 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]

(137, 202, 359)-Net over F₃ — Digital

Digital (137, 202, 359)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 202, 6318)-Net in Base 3 — Upper bound on s

There is no (137, 202, 6319)-net in base 3, because

1 times m-reduction [i] would yield (137, 201, 6319)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 798912 257573 383324 784707 318488 456473 484082 438319 962575 400172 804900 116944 644822 994819 889102 439361 > 3²⁰¹ [i]