MinT - Best Known (45, 45+48, s)-Nets in Base 16

Best Known (45, 45+48, s)-Nets in Base 16

(45, 45+48, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 93, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 93, 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]

(45, 45+48, 288)-Net over F₁₆ — Digital

Digital (45, 93, 288)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+48, 30272)-Net in Base 16 — Upper bound on s

There is no (45, 93, 30273)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9623 310521 510744 592871 338862 110339 929766 207656 875897 548164 080151 190558 130480 583784 305419 074269 341419 814392 597256 > 16⁹³ [i]