MinT - Best Known (57, 57+42, s)-Nets in Base 4

Best Known (57, 57+42, s)-Nets in Base 4

(57, 57+42, 130)-Net over F₄ — Constructive and digital

Digital (57, 99, 130)-net over F₄, using

3 times m-reduction [i] based on digital (57, 102, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 51, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(57, 57+42, 134)-Net over F₄ — Digital

Digital (57, 99, 134)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+42, 1976)-Net in Base 4 — Upper bound on s

There is no (57, 99, 1977)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 402879 941347 209111 184717 123425 324287 213146 444971 838198 472032 > 4⁹⁹ [i]