MinT - Best Known (61, 61+71, s)-Nets in Base 5

Best Known (61, 61+71, s)-Nets in Base 5

(61, 61+71, 82)-Net over F₅ — Constructive and digital

Digital (61, 132, 82)-net over F₅, using

t-expansion [i] based on digital (48, 132, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(61, 61+71, 120)-Net over F₅ — Digital

Digital (61, 132, 120)-net over F₅, using

net from sequence [i] based on digital (61, 119)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(61, 61+71, 1411)-Net in Base 5 — Upper bound on s

There is no (61, 132, 1412)-net in base 5, because

1 times m-reduction [i] would yield (61, 131, 1412)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 37 588766 599852 628649 775694 266758 597200 971189 420289 504069 343788 387785 030221 922594 119614 785809 > 5¹³¹ [i]