MinT - Best Known (23, 44, s)-Nets in Base 8

Best Known (23, 44, s)-Nets in Base 8

(23, 44, 160)-Net over F₈ — Constructive and digital

Digital (23, 44, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 22, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(23, 44, 162)-Net over F₈ — Digital

Digital (23, 44, 162)-net over F₈, using

trace code for nets [i] based on digital (1, 22, 81)-net over F₆₄, using
- net from sequence [i] based on digital (1, 80)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 81, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(23, 44, 4939)-Net in Base 8 — Upper bound on s

There is no (23, 44, 4940)-net in base 8, because

1 times m-reduction [i] would yield (23, 43, 4940)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 681 857672 719311 768054 626862 087980 769267 > 8⁴³ [i]