MinT - Best Known (70−34, 70, s)-Nets in Base 16

Best Known (70−34, 70, s)-Nets in Base 16

(70−34, 70, 516)-Net over F₁₆ — Constructive and digital

Digital (36, 70, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 35, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(70−34, 70, 578)-Net over F₁₆ — Digital

Digital (36, 70, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 35, 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]

(70−34, 70, 43441)-Net in Base 16 — Upper bound on s

There is no (36, 70, 43442)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 943129 076125 110333 537569 767274 197824 963290 089097 148078 616343 792321 426270 502696 970761 > 16⁷⁰ [i]