MinT - Best Known (72−38, 72, s)-Nets in Base 25

Best Known (72−38, 72, s)-Nets in Base 25

(72−38, 72, 204)-Net over F₂₅ — Constructive and digital

Digital (34, 72, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 72, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(72−38, 72, 325)-Net over F₂₅ — Digital

Digital (34, 72, 325)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−38, 72, 65523)-Net in Base 25 — Upper bound on s

There is no (34, 72, 65524)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 44849 701361 959800 130005 662810 658356 731068 475970 847000 373576 028842 473935 232030 268766 351100 835976 000545 > 25⁷² [i]