MinT - Best Known (73−37, 73, s)-Nets in Base 25

Best Known (73−37, 73, s)-Nets in Base 25

(73−37, 73, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 73, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 73, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(73−37, 73, 420)-Net over F₂₅ — Digital

Digital (36, 73, 420)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−37, 73, 122926)-Net in Base 25 — Upper bound on s

There is no (36, 73, 122927)-net in base 25, because

1 times m-reduction [i] would yield (36, 72, 122927)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 44843 616101 057495 796056 766238 153892 250456 034716 540037 862554 479559 927685 863504 651335 229565 624195 033425 > 25⁷² [i]