MinT - Best Known (89−61, 89, s)-Nets in Base 25

Best Known (89−61, 89, s)-Nets in Base 25

(89−61, 89, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 89, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 89, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(89−61, 89, 6311)-Net in Base 25 — Upper bound on s

There is no (28, 89, 6312)-net in base 25, because

1 times m-reduction [i] would yield (28, 88, 6312)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1047 461885 471832 348274 301314 895220 545005 616441 797726 403996 725719 478330 891212 554293 445111 305623 171428 654838 310298 285597 751169 > 25⁸⁸ [i]