MinT - Best Known (128−56, 128, s)-Nets in Base 16

Best Known (128−56, 128, s)-Nets in Base 16

(128−56, 128, 530)-Net over F₁₆ — Constructive and digital

Digital (72, 128, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 64, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(128−56, 128, 1026)-Net over F₁₆ — Digital

Digital (72, 128, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 64, 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]

(128−56, 128, 240676)-Net in Base 16 — Upper bound on s

There is no (72, 128, 240677)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13407 854912 130371 379464 622191 718157 602368 014359 242443 998197 514819 688027 367579 530306 950974 865930 130003 302811 570297 389129 942954 688247 090793 605068 982086 256116 > 16¹²⁸ [i]