MinT - Best Known (55, 81, s)-Nets in Base 4

Best Known (55, 81, s)-Nets in Base 4

(55, 81, 240)-Net over F₄ — Constructive and digital

Digital (55, 81, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 27, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(55, 81, 315)-Net over F₄ — Digital

Digital (55, 81, 315)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 81, 10645)-Net in Base 4 — Upper bound on s

There is no (55, 81, 10646)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 850530 989603 711035 363813 674087 474135 718193 723294 > 4⁸¹ [i]