MinT - Best Known (24, 24+19, s)-Nets in Base 8

Best Known (24, 24+19, s)-Nets in Base 8

(24, 24+19, 160)-Net over F₈ — Constructive and digital

Digital (24, 43, 160)-net over F₈, using

3 times m-reduction [i] based on digital (24, 46, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 23, 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]

(24, 24+19, 194)-Net over F₈ — Digital

Digital (24, 43, 194)-net over F₈, using

1 times m-reduction [i] based on digital (24, 44, 194)-net over F₈, using
- trace code for nets [i] based on digital (2, 22, 97)-net over F₆₄, using
  - net from sequence [i] based on digital (2, 96)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 2 and N(F) ≥ 97, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(24, 24+19, 9701)-Net in Base 8 — Upper bound on s

There is no (24, 43, 9702)-net in base 8, because

1 times m-reduction [i] would yield (24, 42, 9702)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85 113658 162573 153121 257697 558804 442596 > 8⁴² [i]