MinT - Best Known (8, 8+6, s)-Nets in Base 8

Best Known (8, 8+6, s)-Nets in Base 8

(8, 8+6, 160)-Net over F₈ — Constructive and digital

Digital (8, 14, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 7, 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]

(8, 8+6, 162)-Net over F₈ — Digital

Digital (8, 14, 162)-net over F₈, using

trace code for nets [i] based on digital (1, 7, 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]

(8, 8+6, 258)-Net in Base 8 — Constructive

(8, 14, 258)-net in base 8, using

trace code for nets [i] based on (1, 7, 129)-net in base 64, using
- base change [i] based on digital (0, 6, 129)-net over F₁₂₈, using
  - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
      - the rational function field F₁₂₈(x) [i]
    - Niederreiter sequence [i]

(8, 8+6, 4251)-Net in Base 8 — Upper bound on s

There is no (8, 14, 4252)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 399063 615731 > 8¹⁴ [i]