MinT - Best Known (56, 56+54, s)-Nets in Base 16

Best Known (56, 56+54, s)-Nets in Base 16

(56, 56+54, 516)-Net over F₁₆ — Constructive and digital

Digital (56, 110, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 55, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(56, 56+54, 578)-Net over F₁₆ — Digital

Digital (56, 110, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 55, 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]

(56, 56+54, 58597)-Net in Base 16 — Upper bound on s

There is no (56, 110, 58598)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 839734 040777 825486 635850 330479 149188 603005 841013 972521 539495 910478 019856 682348 054712 762021 017129 389217 853377 396317 874336 305144 127416 > 16¹¹⁰ [i]