MinT - Best Known (41, 41+31, s)-Nets in Base 4

Best Known (41, 41+31, s)-Nets in Base 4

(41, 41+31, 98)-Net over F₄ — Constructive and digital

Digital (41, 72, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 36, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(41, 41+31, 101)-Net over F₄ — Digital

Digital (41, 72, 101)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+31, 1502)-Net in Base 4 — Upper bound on s

There is no (41, 72, 1503)-net in base 4, because

1 times m-reduction [i] would yield (41, 71, 1503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 576354 586449 088889 101693 199736 845535 327044 > 4⁷¹ [i]