MinT - Best Known (98−56, 98, s)-Nets in Base 16

Best Known (98−56, 98, s)-Nets in Base 16

(98−56, 98, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 98, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 98, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(98−56, 98, 12325)-Net in Base 16 — Upper bound on s

There is no (42, 98, 12326)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10106 035925 588118 168648 075061 806344 881301 037891 919668 381664 543197 271888 516847 918646 574772 877654 952276 210339 094010 386596 > 16⁹⁸ [i]