MinT - Best Known (85−68, 85, s)-Nets in Base 25

Best Known (85−68, 85, s)-Nets in Base 25

(85−68, 85, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 85, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 85, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(85−68, 85, 150)-Net over F₂₅ — Digital

Digital (17, 85, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 85, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(85−68, 85, 1744)-Net in Base 25 — Upper bound on s

There is no (17, 85, 1745)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 67383 670063 708958 601896 532365 753850 304242 838354 964377 075290 730493 310131 413242 196682 459301 702589 553685 006551 421699 106417 > 25⁸⁵ [i]