MinT - Best Known (64, 64+62, s)-Nets in Base 16

Best Known (64, 64+62, s)-Nets in Base 16

(64, 64+62, 516)-Net over F₁₆ — Constructive and digital

Digital (64, 126, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 63, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(64, 64+62, 578)-Net over F₁₆ — Digital

Digital (64, 126, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 63, 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]

(64, 64+62, 64862)-Net in Base 16 — Upper bound on s

There is no (64, 126, 64863)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 391030 333002 443441 803143 200753 294217 690396 027670 141458 018762 379074 920985 220857 940056 628977 229129 514562 374538 696160 450944 073042 064058 919030 041379 885296 > 16¹²⁶ [i]