MinT - Best Known (65−33, 65, s)-Nets in Base 25

Best Known (65−33, 65, s)-Nets in Base 25

(65−33, 65, 204)-Net over F₂₅ — Constructive and digital

Digital (32, 65, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 65, 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]

(65−33, 65, 384)-Net over F₂₅ — Digital

Digital (32, 65, 384)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−33, 65, 110676)-Net in Base 25 — Upper bound on s

There is no (32, 65, 110677)-net in base 25, because

1 times m-reduction [i] would yield (32, 64, 110677)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 293894 215472 190676 056832 777587 318958 855057 517472 850188 577142 642738 178773 765289 036602 818945 > 25⁶⁴ [i]