MinT - Best Known (244−89, 244, s)-Nets in Base 3

Best Known (244−89, 244, s)-Nets in Base 3

(244−89, 244, 162)-Net over F₃ — Constructive and digital

Digital (155, 244, 162)-net over F₃, using

2 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 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]

(244−89, 244, 290)-Net over F₃ — Digital

Digital (155, 244, 290)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−89, 244, 3679)-Net in Base 3 — Upper bound on s

There is no (155, 244, 3680)-net in base 3, because

1 times m-reduction [i] would yield (155, 243, 3680)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 397376 137511 827590 950232 282808 112518 031087 202425 996990 912690 719252 993328 744500 488242 640001 048432 257994 163023 870209 > 3²⁴³ [i]