MinT - Best Known (90−44, 90, s)-Nets in Base 16

Best Known (90−44, 90, s)-Nets in Base 16

(90−44, 90, 516)-Net over F₁₆ — Constructive and digital

Digital (46, 90, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 45, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(90−44, 90, 578)-Net over F₁₆ — Digital

Digital (46, 90, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 45, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(90−44, 90, 50886)-Net in Base 16 — Upper bound on s

There is no (46, 90, 50887)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 348757 682493 321575 862737 869252 559568 671042 682135 803691 387565 690272 930109 883922 124957 793104 733177 106069 833636 > 16⁹⁰ [i]