MinT - Best Known (44−21, 44, s)-Nets in Base 4

Best Known (44−21, 44, s)-Nets in Base 4

(44−21, 44, 48)-Net over F₄ — Constructive and digital

Digital (23, 44, 48)-net over F₄, using

trace code for nets [i] based on digital (1, 22, 24)-net over F₁₆, using
- net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(44−21, 44, 52)-Net over F₄ — Digital

Digital (23, 44, 52)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−21, 44, 577)-Net in Base 4 — Upper bound on s

There is no (23, 44, 578)-net in base 4, because

1 times m-reduction [i] would yield (23, 43, 578)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 77 426011 579628 476281 652576 > 4⁴³ [i]