MinT - Best Known (102−43, 102, s)-Nets in Base 16

Best Known (102−43, 102, s)-Nets in Base 16

(102−43, 102, 530)-Net over F₁₆ — Constructive and digital

Digital (59, 102, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 51, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(102−43, 102, 1026)-Net over F₁₆ — Digital

Digital (59, 102, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 51, 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]

(102−43, 102, 357792)-Net in Base 16 — Upper bound on s

There is no (59, 102, 357793)-net in base 16, because

1 times m-reduction [i] would yield (59, 101, 357793)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 317281 651140 317432 428324 837574 222546 433751 606983 117950 662830 621702 607165 171457 347537 619001 941615 631268 551300 221850 603296 > 16¹⁰¹ [i]