MinT - Best Known (69−49, 69, s)-Nets in Base 25

Best Known (69−49, 69, s)-Nets in Base 25

(69−49, 69, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 69, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 69, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(69−49, 69, 171)-Net over F₂₅ — Digital

Digital (20, 69, 171)-net over F₂₅, using

net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
  - an algebraic function field by Teo [i]

(69−49, 69, 3719)-Net in Base 25 — Upper bound on s

There is no (20, 69, 3720)-net in base 25, because

1 times m-reduction [i] would yield (20, 68, 3720)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 114903 393805 409683 841077 295516 970470 568334 149094 056169 949248 241505 529905 984273 426653 038422 787585 > 25⁶⁸ [i]