MinT - Best Known (171−56, 171, s)-Nets in Base 4

Best Known (171−56, 171, s)-Nets in Base 4

(171−56, 171, 240)-Net over F₄ — Constructive and digital

Digital (115, 171, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 57, 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]

(171−56, 171, 514)-Net over F₄ — Digital

Digital (115, 171, 514)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−56, 171, 17872)-Net in Base 4 — Upper bound on s

There is no (115, 171, 17873)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 959847 916217 359549 563094 193894 633619 059846 989987 430967 581608 413327 778375 406608 691363 275023 790473 012560 > 4¹⁷¹ [i]