MinT - Best Known (27, 27+65, s)-Nets in Base 25

Best Known (27, 27+65, s)-Nets in Base 25

(27, 27+65, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 92, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 92, 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]

(27, 27+65, 5018)-Net in Base 25 — Upper bound on s

There is no (27, 92, 5019)-net in base 25, because

1 times m-reduction [i] would yield (27, 91, 5019)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 16 324353 797873 543666 106817 004850 445473 781494 240693 562114 955689 739214 860178 445146 939269 175214 763968 994147 716673 114431 664590 727425 > 25⁹¹ [i]