MinT - Best Known (223−106, 223, s)-Nets in Base 3

Best Known (223−106, 223, s)-Nets in Base 3

(223−106, 223, 76)-Net over F₃ — Constructive and digital

Digital (117, 223, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (32, 85, 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, 138, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃ (see above)

(223−106, 223, 127)-Net over F₃ — Digital

Digital (117, 223, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−106, 223, 996)-Net in Base 3 — Upper bound on s

There is no (117, 223, 997)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25841 877891 071031 391948 157913 222536 731678 501971 881243 365801 827561 968818 282451 907288 845738 519198 617862 087451 > 3²²³ [i]