MinT - Best Known (129−92, 129, s)-Nets in Base 5

Best Known (129−92, 129, s)-Nets in Base 5

(129−92, 129, 72)-Net over F₅ — Constructive and digital

Digital (37, 129, 72)-net over F₅, using

t-expansion [i] based on digital (31, 129, 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]

(129−92, 129, 76)-Net over F₅ — Digital

Digital (37, 129, 76)-net over F₅, using

t-expansion [i] based on digital (34, 129, 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]

(129−92, 129, 377)-Net in Base 5 — Upper bound on s

There is no (37, 129, 378)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 558667 841542 715643 293842 033590 407498 654663 919920 778809 784535 046880 232607 237921 723582 804225 > 5¹²⁹ [i]