MinT - Best Known (37, 102, s)-Nets in Base 5

Best Known (37, 102, s)-Nets in Base 5

(37, 102, 72)-Net over F₅ — Constructive and digital

Digital (37, 102, 72)-net over F₅, using

t-expansion [i] based on digital (31, 102, 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]

(37, 102, 76)-Net over F₅ — Digital

Digital (37, 102, 76)-net over F₅, using

t-expansion [i] based on digital (34, 102, 76)-net over F₅, using
- net from sequence [i] based on digital (34, 75)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(37, 102, 490)-Net in Base 5 — Upper bound on s

There is no (37, 102, 491)-net in base 5, because

1 times m-reduction [i] would yield (37, 101, 491)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 39803 518578 039603 170898 286508 462780 024565 673211 830085 039640 408122 862465 > 5¹⁰¹ [i]