MinT - Best Known (43, 82, s)-Nets in Base 9

Best Known (43, 82, s)-Nets in Base 9

(43, 82, 232)-Net over F₉ — Constructive and digital

Digital (43, 82, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 41, 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]

(43, 82, 236)-Net over F₉ — Digital

Digital (43, 82, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 41, 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]

(43, 82, 11582)-Net in Base 9 — Upper bound on s

There is no (43, 82, 11583)-net in base 9, because

1 times m-reduction [i] would yield (43, 81, 11583)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196930 166592 085511 926749 015277 866614 057321 988620 345814 609437 140722 863407 752553 > 9⁸¹ [i]