MinT - Best Known (86−42, 86, s)-Nets in Base 16

Best Known (86−42, 86, s)-Nets in Base 16

(86−42, 86, 516)-Net over F₁₆ — Constructive and digital

Digital (44, 86, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(86−42, 86, 578)-Net over F₁₆ — Digital

Digital (44, 86, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 43, 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]

(86−42, 86, 49369)-Net in Base 16 — Upper bound on s

There is no (44, 86, 49370)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 35 842951 900109 693341 847596 158510 604151 395339 305661 252509 715463 495212 868949 060241 319506 550016 028630 520926 > 16⁸⁶ [i]