MinT - Best Known (99, 99+104, s)-Nets in Base 3

Best Known (99, 99+104, s)-Nets in Base 3

(99, 99+104, 68)-Net over F₃ — Constructive and digital

Digital (99, 203, 68)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (21, 73, 32)-net over F₃, using
  - net from sequence [i] based on digital (21, 31)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
      - an explicitly constructive algebraic function field [i]
2. digital (26, 130, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]

(99, 99+104, 96)-Net over F₃ — Digital

Digital (99, 203, 96)-net over F₃, using

t-expansion [i] based on digital (89, 203, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(99, 99+104, 686)-Net in Base 3 — Upper bound on s

There is no (99, 203, 687)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 192937 300843 578531 119547 383900 428091 098444 942597 910470 238887 208561 027460 054534 062796 088879 818137 > 3²⁰³ [i]