MinT - Best Known (214−100, 214, s)-Nets in Base 3

Best Known (214−100, 214, s)-Nets in Base 3

(214−100, 214, 76)-Net over F₃ — Constructive and digital

Digital (114, 214, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (32, 82, 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, 132, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃ (see above)

(214−100, 214, 128)-Net over F₃ — Digital

Digital (114, 214, 128)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−100, 214, 1024)-Net in Base 3 — Upper bound on s

There is no (114, 214, 1025)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 288178 542995 743492 406081 267705 951528 439910 869634 084746 304503 181605 805681 635427 030245 922699 614210 591689 > 3²¹⁴ [i]