MinT - Best Known (130−64, 130, s)-Nets in Base 16

Best Known (130−64, 130, s)-Nets in Base 16

(130−64, 130, 516)-Net over F₁₆ — Constructive and digital

Digital (66, 130, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 65, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(130−64, 130, 578)-Net over F₁₆ — Digital

Digital (66, 130, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 65, 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]

(130−64, 130, 66437)-Net in Base 16 — Upper bound on s

There is no (66, 130, 66438)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 433728 379378 825944 316800 967436 839827 588754 301814 218980 130116 572666 711239 096678 578346 186930 350173 568653 782294 663416 239860 743790 379892 880284 311968 362467 647716 > 16¹³⁰ [i]