MinT - Best Known (81, 117, s)-Nets in Base 4

Best Known (81, 117, s)-Nets in Base 4

(81, 117, 312)-Net over F₄ — Constructive and digital

Digital (81, 117, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 39, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(81, 117, 487)-Net over F₄ — Digital

Digital (81, 117, 487)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 117, 20610)-Net in Base 4 — Upper bound on s

There is no (81, 117, 20611)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27613 458646 153044 124948 691265 578933 869425 577788 013155 761417 695681 602040 > 4¹¹⁷ [i]