MinT - Best Known (114−56, 114, s)-Nets in Base 16

Best Known (114−56, 114, s)-Nets in Base 16

(114−56, 114, 516)-Net over F₁₆ — Constructive and digital

Digital (58, 114, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 57, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(114−56, 114, 578)-Net over F₁₆ — Digital

Digital (58, 114, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 57, 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]

(114−56, 114, 60157)-Net in Base 16 — Upper bound on s

There is no (58, 114, 60158)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 186095 097092 196190 606113 662239 774561 123733 931786 324774 248261 928277 013903 710725 552505 511020 637488 049991 781653 659378 326363 586342 706817 309411 > 16¹¹⁴ [i]