MinT - Best Known (42, 90, s)-Nets in Base 16

Best Known (42, 90, s)-Nets in Base 16

(42, 90, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 90, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 90, 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]

(42, 90, 238)-Net over F₁₆ — Digital

Digital (42, 90, 238)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 90, 257)-Net in Base 16

(42, 90, 257)-net in base 16, using

base change [i] based on digital (12, 60, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(42, 90, 21402)-Net in Base 16 — Upper bound on s

There is no (42, 90, 21403)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 351001 047171 784286 148765 283514 220192 342577 436592 607366 036046 765692 790675 085974 286274 618912 430720 603113 165181 > 16⁹⁰ [i]