MinT - Best Known (129−86, 129, s)-Nets in Base 5

Best Known (129−86, 129, s)-Nets in Base 5

(129−86, 129, 78)-Net over F₅ — Constructive and digital

Digital (43, 129, 78)-net over F₅, using

t-expansion [i] based on digital (38, 129, 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]

(129−86, 129, 84)-Net over F₅ — Digital

Digital (43, 129, 84)-net over F₅, using

net from sequence [i] based on digital (43, 83)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(129−86, 129, 496)-Net in Base 5 — Upper bound on s

There is no (43, 129, 497)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 527061 152844 786471 807857 250360 152556 740854 876163 561530 267413 296975 960333 289054 769518 725405 > 5¹²⁹ [i]