MinT - Best Known (99−58, 99, s)-Nets in Base 5

Best Known (99−58, 99, s)-Nets in Base 5

(99−58, 99, 78)-Net over F₅ — Constructive and digital

Digital (41, 99, 78)-net over F₅, using

t-expansion [i] based on digital (38, 99, 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]

(99−58, 99, 80)-Net over F₅ — Digital

Digital (41, 99, 80)-net over F₅, using

net from sequence [i] based on digital (41, 79)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 41 and N(F) ≥ 80, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(99−58, 99, 688)-Net in Base 5 — Upper bound on s

There is no (41, 99, 689)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1585 412304 483113 689833 491251 599960 739029 921043 855188 480319 108631 134485 > 5⁹⁹ [i]