MinT - Best Known (52, 52+48, s)-Nets in Base 9

Best Known (52, 52+48, s)-Nets in Base 9

(52, 52+48, 232)-Net over F₉ — Constructive and digital

Digital (52, 100, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 50, 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]

(52, 52+48, 236)-Net over F₉ — Digital

Digital (52, 100, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 50, 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]

(52, 52+48, 11580)-Net in Base 9 — Upper bound on s

There is no (52, 100, 11581)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 265703 135570 923415 176880 244478 676109 685804 911559 022475 599505 903496 502766 839381 961447 574560 132289 > 9¹⁰⁰ [i]