MinT - Best Known (118−58, 118, s)-Nets in Base 16

Best Known (118−58, 118, s)-Nets in Base 16

(118−58, 118, 516)-Net over F₁₆ — Constructive and digital

Digital (60, 118, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 59, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(118−58, 118, 578)-Net over F₁₆ — Digital

Digital (60, 118, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 59, 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]

(118−58, 118, 61722)-Net in Base 16 — Upper bound on s

There is no (60, 118, 61723)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12198 937773 750875 929129 823762 301581 147090 240424 323869 316805 622119 889927 907882 052835 312557 211516 514275 316236 554116 443549 600811 633488 729773 225856 > 16¹¹⁸ [i]