MinT - Best Known (66, 116, s)-Nets in Base 16

Best Known (66, 116, s)-Nets in Base 16

(66, 116, 530)-Net over F₁₆ — Constructive and digital

Digital (66, 116, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 58, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(66, 116, 1026)-Net over F₁₆ — Digital

Digital (66, 116, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 58, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(66, 116, 262197)-Net in Base 16 — Upper bound on s

There is no (66, 116, 262198)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 636085 351002 879993 417302 968265 287761 142364 422494 772946 610529 280130 202855 528557 063912 314280 799445 144932 805605 085689 462176 193347 795156 344876 > 16¹¹⁶ [i]