MinT - Best Known (48, 48+44, s)-Nets in Base 4

Best Known (48, 48+44, s)-Nets in Base 4

(48, 48+44, 66)-Net over F₄ — Constructive and digital

Digital (48, 92, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 46, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(48, 48+44, 87)-Net over F₄ — Digital

Digital (48, 92, 87)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+44, 976)-Net in Base 4 — Upper bound on s

There is no (48, 92, 977)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24 844684 513831 255587 778181 867858 677669 310928 033910 000480 > 4⁹² [i]