MinT - Best Known (39, 82, s)-Nets in Base 25

Best Known (39, 82, s)-Nets in Base 25

(39, 82, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 82, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 82, 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]

(39, 82, 371)-Net over F₂₅ — Digital

Digital (39, 82, 371)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 82, 89183)-Net in Base 25 — Upper bound on s

There is no (39, 82, 89184)-net in base 25, because

1 times m-reduction [i] would yield (39, 81, 89184)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 171092 139866 080511 300789 736992 169041 593340 143712 603371 399992 571778 525605 666907 105392 469306 559484 241370 218727 830785 > 25⁸¹ [i]