MinT - Best Known (57−28, 57, s)-Nets in Base 5

Best Known (57−28, 57, s)-Nets in Base 5

(57−28, 57, 52)-Net over F₅ — Constructive and digital

Digital (29, 57, 52)-net over F₅, using

1 times m-reduction [i] based on digital (29, 58, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 29, 26)-net over F₂₅, using
  - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
      - the rational function field F₂₅(x) [i]
    - Niederreiter sequence [i]

(57−28, 57, 73)-Net over F₅ — Digital

Digital (29, 57, 73)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−28, 57, 1049)-Net in Base 5 — Upper bound on s

There is no (29, 57, 1050)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6958 516230 804077 744063 059206 540273 071361 > 5⁵⁷ [i]