MinT - Best Known (52, 88, s)-Nets in Base 16

Best Known (52, 88, s)-Nets in Base 16

(52, 88, 530)-Net over F₁₆ — Constructive and digital

Digital (52, 88, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 44, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(52, 88, 1026)-Net over F₁₆ — Digital

Digital (52, 88, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 44, 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]

(52, 88, 388004)-Net in Base 16 — Upper bound on s

There is no (52, 88, 388005)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9174 214023 560780 911691 257373 608024 183525 981271 180771 682387 062622 856148 202369 272730 289497 837005 362014 911476 > 16⁸⁸ [i]