MinT - Best Known (100−56, 100, s)-Nets in Base 16

Best Known (100−56, 100, s)-Nets in Base 16

(100−56, 100, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 100, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 100, 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]

(100−56, 100, 226)-Net over F₁₆ — Digital

Digital (44, 100, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 100, 226)-net over F₁₆, using
- net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
    - Drinfeld modules of rank 1 [i]

(100−56, 100, 15027)-Net in Base 16 — Upper bound on s

There is no (44, 100, 15028)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 582690 624759 685763 520889 757339 910051 439364 143619 401959 313610 599129 269764 248691 876530 431616 676374 424583 196758 804267 278936 > 16¹⁰⁰ [i]