MinT - Best Known (17, 73, s)-Nets in Base 25

Best Known (17, 73, s)-Nets in Base 25

(17, 73, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 73, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 73, 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]

(17, 73, 150)-Net over F₂₅ — Digital

Digital (17, 73, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 73, 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]

(17, 73, 2062)-Net in Base 25 — Upper bound on s

There is no (17, 73, 2063)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 131775 919665 916980 603614 437281 591800 370861 997859 844786 085907 878671 137107 388396 287527 231975 876079 309665 > 25⁷³ [i]