MinT - Best Known (47, 124, s)-Nets in Base 5

Best Known (47, 124, s)-Nets in Base 5

(47, 124, 78)-Net over F₅ — Constructive and digital

Digital (47, 124, 78)-net over F₅, using

t-expansion [i] based on digital (38, 124, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(47, 124, 92)-Net over F₅ — Digital

Digital (47, 124, 92)-net over F₅, using

net from sequence [i] based on digital (47, 91)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(47, 124, 659)-Net in Base 5 — Upper bound on s

There is no (47, 124, 660)-net in base 5, because

1 times m-reduction [i] would yield (47, 123, 660)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 95 180743 595671 659526 804099 191193 442486 320798 232483 666270 801307 518499 286721 053696 754625 > 5¹²³ [i]