MinT - Best Known (50, 98, s)-Nets in Base 16

Best Known (50, 98, s)-Nets in Base 16

(50, 98, 516)-Net over F₁₆ — Constructive and digital

Digital (50, 98, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 49, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(50, 98, 578)-Net over F₁₆ — Digital

Digital (50, 98, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 49, 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]

(50, 98, 53949)-Net in Base 16 — Upper bound on s

There is no (50, 98, 53950)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10088 108924 872458 435833 218291 280188 009662 590803 205397 306272 865866 259338 868203 482307 415479 473510 984950 343961 697472 407001 > 16⁹⁸ [i]