MinT - Best Known (44, 44+44, s)-Nets in Base 16

Best Known (44, 44+44, s)-Nets in Base 16

(44, 44+44, 514)-Net over F₁₆ — Constructive and digital

Digital (44, 88, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 44, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(44, 44+44, 39546)-Net in Base 16 — Upper bound on s

There is no (44, 88, 39547)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9175 495687 768817 917861 171378 382724 726143 973559 892824 027150 685946 571817 047258 301551 351560 435234 311077 090186 > 16⁸⁸ [i]