MinT - Best Known (48, 48+46, s)-Nets in Base 16

Best Known (48, 48+46, s)-Nets in Base 16

(48, 48+46, 516)-Net over F₁₆ — Constructive and digital

Digital (48, 94, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 47, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(48, 48+46, 578)-Net over F₁₆ — Digital

Digital (48, 94, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 47, 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]

(48, 48+46, 52413)-Net in Base 16 — Upper bound on s

There is no (48, 94, 52414)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 153914 888959 037116 055886 410443 761369 239879 178954 791527 918966 206731 640598 847628 400503 037498 251251 414710 500122 564956 > 16⁹⁴ [i]