MinT - Best Known (88−42, 88, s)-Nets in Base 9

Best Known (88−42, 88, s)-Nets in Base 9

(88−42, 88, 232)-Net over F₉ — Constructive and digital

Digital (46, 88, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 44, 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]

(88−42, 88, 236)-Net over F₉ — Digital

Digital (46, 88, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 44, 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]

(88−42, 88, 10805)-Net in Base 9 — Upper bound on s

There is no (46, 88, 10806)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 942226 905501 748291 304407 881203 808878 866426 435754 480916 976735 638959 115638 245197 282801 > 9⁸⁸ [i]