MinT - Best Known (220−68, 220, s)-Nets in Base 3

Best Known (220−68, 220, s)-Nets in Base 3

(220−68, 220, 204)-Net over F₃ — Constructive and digital

Digital (152, 220, 204)-net over F₃, using

3¹ times duplication [i] based on digital (151, 219, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 73, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(220−68, 220, 438)-Net over F₃ — Digital

Digital (152, 220, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−68, 220, 8240)-Net in Base 3 — Upper bound on s

There is no (152, 220, 8241)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 928 911224 514810 938905 466835 077487 788701 523039 676699 870472 503219 644916 573195 744789 827373 568937 799744 520809 > 3²²⁰ [i]