MinT - Best Known (52, 98, s)-Nets in Base 4

Best Known (52, 98, s)-Nets in Base 4

(52, 98, 76)-Net over F₄ — Constructive and digital

Digital (52, 98, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 49, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(52, 98, 97)-Net over F₄ — Digital

Digital (52, 98, 97)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 98, 1136)-Net in Base 4 — Upper bound on s

There is no (52, 98, 1137)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 101262 029850 765795 285146 192767 754712 494296 801572 244832 547808 > 4⁹⁸ [i]