MinT - Best Known (56, 96, s)-Nets in Base 16

Best Known (56, 96, s)-Nets in Base 16

(56, 96, 530)-Net over F₁₆ — Constructive and digital

Digital (56, 96, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 48, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(56, 96, 1026)-Net over F₁₆ — Digital

Digital (56, 96, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 48, 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]

(56, 96, 333408)-Net in Base 16 — Upper bound on s

There is no (56, 96, 333409)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 402988 638065 161225 188960 521790 640171 355559 660016 835349 443993 518395 119738 164199 511910 114730 788710 925348 462693 699576 > 16⁹⁶ [i]