MinT - Best Known (210−104, 210, s)-Nets in Base 3

Best Known (210−104, 210, s)-Nets in Base 3

(210−104, 210, 74)-Net over F₃ — Constructive and digital

Digital (106, 210, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 79, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [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 (27, 131, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(210−104, 210, 107)-Net over F₃ — Digital

Digital (106, 210, 107)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−104, 210, 804)-Net in Base 3 — Upper bound on s

There is no (106, 210, 805)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16432 597005 920133 696409 283493 776624 453789 486454 887749 008824 815645 251550 963595 092284 002922 082412 786577 > 3²¹⁰ [i]