MinT - Best Known (76, 147, s)-Nets in Base 5

Best Known (76, 147, s)-Nets in Base 5

(76, 147, 98)-Net over F₅ — Constructive and digital

Digital (76, 147, 98)-net over F₅, using

1 times m-reduction [i] based on digital (76, 148, 98)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 45, 26)-net over F₅, using
    - net from sequence [i] based on digital (9, 25)-sequence over F₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
        an explicitly constructive algebraic function field [i]
  2. digital (31, 103, 72)-net over F₅, using
    - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
        an explicitly constructive algebraic function field [i]

(76, 147, 161)-Net over F₅ — Digital

Digital (76, 147, 161)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 147, 2837)-Net in Base 5 — Upper bound on s

There is no (76, 147, 2838)-net in base 5, because

1 times m-reduction [i] would yield (76, 146, 2838)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 122427 820091 772571 520737 641554 381935 386039 648216 501682 002740 296485 183044 661152 302377 064904 235608 203897 > 5¹⁴⁶ [i]