MinT - Best Known (211−98, 211, s)-Nets in Base 3

Best Known (211−98, 211, s)-Nets in Base 3

(211−98, 211, 76)-Net over F₃ — Constructive and digital

Digital (113, 211, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (32, 81, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
      - an explicitly constructive algebraic function field [i]
2. digital (32, 130, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃ (see above)

(211−98, 211, 129)-Net over F₃ — Digital

Digital (113, 211, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−98, 211, 1035)-Net in Base 3 — Upper bound on s

There is no (113, 211, 1036)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47344 133241 581837 377217 569280 426574 486231 590327 843293 549382 390653 497229 386019 840221 911069 260753 671705 > 3²¹¹ [i]