MinT - Best Known (36−16, 36, s)-Nets in Base 9

Best Known (36−16, 36, s)-Nets in Base 9

(36−16, 36, 232)-Net over F₉ — Constructive and digital

Digital (20, 36, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 18, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(36−16, 36, 236)-Net over F₉ — Digital

Digital (20, 36, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 18, 118)-net over F₈₁, using
- net from sequence [i] based on digital (2, 117)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(36−16, 36, 9257)-Net in Base 9 — Upper bound on s

There is no (20, 36, 9258)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22543 683298 155607 163802 972486 310785 > 9³⁶ [i]