MinT - Best Known (126−41, 126, s)-Nets in Base 4

Best Known (126−41, 126, s)-Nets in Base 4

(126−41, 126, 240)-Net over F₄ — Constructive and digital

Digital (85, 126, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 42, 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]

(126−41, 126, 410)-Net over F₄ — Digital

Digital (85, 126, 410)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−41, 126, 16018)-Net in Base 4 — Upper bound on s

There is no (85, 126, 16019)-net in base 4, because

1 times m-reduction [i] would yield (85, 125, 16019)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1810 367024 615367 368181 108784 899731 851084 899638 656713 955899 810395 598972 598144 > 4¹²⁵ [i]