MinT - Best Known (35, 35+33, s)-Nets in Base 8

Best Known (35, 35+33, s)-Nets in Base 8

(35, 35+33, 160)-Net over F₈ — Constructive and digital

Digital (35, 68, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 34, 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]

(35, 35+33, 162)-Net over F₈ — Digital

Digital (35, 68, 162)-net over F₈, using

trace code for nets [i] based on digital (1, 34, 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]

(35, 35+33, 5866)-Net in Base 8 — Upper bound on s

There is no (35, 68, 5867)-net in base 8, because

1 times m-reduction [i] would yield (35, 67, 5867)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 214997 617999 545617 510203 428712 277427 124929 140982 200630 934270 > 8⁶⁷ [i]