MinT - Best Known (64−20, 64, s)-Nets in Base 3

Best Known (64−20, 64, s)-Nets in Base 3

(64−20, 64, 114)-Net over F₃ — Constructive and digital

Digital (44, 64, 114)-net over F₃, using

3¹ times duplication [i] based on digital (43, 63, 114)-net over F₃, using
- trace code for nets [i] based on digital (1, 21, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(64−20, 64, 163)-Net over F₃ — Digital

Digital (44, 64, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−20, 64, 2552)-Net in Base 3 — Upper bound on s

There is no (44, 64, 2553)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 444694 093794 993219 895609 129049 > 3⁶⁴ [i]