MinT - Best Known (100−42, 100, s)-Nets in Base 16

Best Known (100−42, 100, s)-Nets in Base 16

(100−42, 100, 530)-Net over F₁₆ — Constructive and digital

Digital (58, 100, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 50, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(100−42, 100, 1026)-Net over F₁₆ — Digital

Digital (58, 100, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 50, 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]

(100−42, 100, 313538)-Net in Base 16 — Upper bound on s

There is no (58, 100, 313539)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 582421 135862 866292 930535 827089 537444 977311 284166 814003 116375 782499 629172 175710 492369 515650 679862 585058 287836 172625 213536 > 16¹⁰⁰ [i]