MinT - Best Known (56, 56+46, s)-Nets in Base 4

Best Known (56, 56+46, s)-Nets in Base 4

(56, 56+46, 98)-Net over F₄ — Constructive and digital

Digital (56, 102, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 51, 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]

(56, 56+46, 113)-Net over F₄ — Digital

Digital (56, 102, 113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+46, 1451)-Net in Base 4 — Upper bound on s

There is no (56, 102, 1452)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25 912258 435119 807552 907472 916312 133133 457529 248703 497300 981988 > 4¹⁰² [i]