MinT - Best Known (202−100, 202, s)-Nets in Base 3

Best Known (202−100, 202, s)-Nets in Base 3

(202−100, 202, 72)-Net over F₃ — Constructive and digital

Digital (102, 202, 72)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 76, 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]
2. digital (26, 126, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃ (see above)

(202−100, 202, 104)-Net over F₃ — Digital

Digital (102, 202, 104)-net over F₃, using

net from sequence [i] based on digital (102, 103)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(202−100, 202, 776)-Net in Base 3 — Upper bound on s

There is no (102, 202, 777)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 506415 533341 661741 372580 588745 673407 034464 142291 842874 525895 930596 391435 002570 990115 506590 490521 > 3²⁰² [i]