MinT - Best Known (18, 18+16, s)-Nets in Base 5

Best Known (18, 18+16, s)-Nets in Base 5

(18, 18+16, 54)-Net over F₅ — Constructive and digital

Digital (18, 34, 54)-net over F₅, using

trace code for nets [i] based on digital (1, 17, 27)-net over F₂₅, using
- net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
  - Niederreiter sequence [i]

(18, 18+16, 72)-Net over F₅ — Digital

Digital (18, 34, 72)-net over F₅, using

trace code for nets [i] based on digital (1, 17, 36)-net over F₂₅, using
- net from sequence [i] based on digital (1, 35)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(18, 18+16, 874)-Net in Base 5 — Upper bound on s

There is no (18, 34, 875)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 587142 402174 369001 535201 > 5³⁴ [i]