MinT - Best Known (78−51, 78, s)-Nets in Base 25

Best Known (78−51, 78, s)-Nets in Base 25

(78−51, 78, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 78, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 78, 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]

(78−51, 78, 8558)-Net in Base 25 — Upper bound on s

There is no (27, 78, 8559)-net in base 25, because

1 times m-reduction [i] would yield (27, 77, 8559)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 438264 642182 564686 570563 073155 238596 685075 943642 414094 459981 464573 188038 380944 682555 977311 958428 820282 668073 > 25⁷⁷ [i]