MinT - Best Known (98−47, 98, s)-Nets in Base 9

Best Known (98−47, 98, s)-Nets in Base 9

(98−47, 98, 232)-Net over F₉ — Constructive and digital

Digital (51, 98, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 49, 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]

(98−47, 98, 236)-Net over F₉ — Digital

Digital (51, 98, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 49, 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]

(98−47, 98, 12453)-Net in Base 9 — Upper bound on s

There is no (51, 98, 12454)-net in base 9, because

1 times m-reduction [i] would yield (51, 97, 12454)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 584064 614103 370892 288139 473155 569646 606257 234493 301719 062336 586891 601547 157257 977496 685457 > 9⁹⁷ [i]