MinT - Best Known (212−87, 212, s)-Nets in Base 3

Best Known (212−87, 212, s)-Nets in Base 3

(212−87, 212, 148)-Net over F₃ — Constructive and digital

Digital (125, 212, 148)-net over F₃, using

4 times m-reduction [i] based on digital (125, 216, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 108, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(212−87, 212, 183)-Net over F₃ — Digital

Digital (125, 212, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−87, 212, 1809)-Net in Base 3 — Upper bound on s

There is no (125, 212, 1810)-net in base 3, because

1 times m-reduction [i] would yield (125, 211, 1810)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47064 549754 304504 252733 267905 598521 578907 361764 098153 450659 198293 626464 601604 202969 941289 097123 606017 > 3²¹¹ [i]