MinT - Best Known (97−45, 97, s)-Nets in Base 4

Best Known (97−45, 97, s)-Nets in Base 4

(97−45, 97, 76)-Net over F₄ — Constructive and digital

Digital (52, 97, 76)-net over F₄, using

1 times m-reduction [i] based on 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]

(97−45, 97, 99)-Net over F₄ — Digital

Digital (52, 97, 99)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−45, 97, 1261)-Net in Base 4 — Upper bound on s

There is no (52, 97, 1262)-net in base 4, because

1 times m-reduction [i] would yield (52, 96, 1262)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6346 948687 731503 739078 304123 034300 324122 803903 319856 975320 > 4⁹⁶ [i]