MinT - Best Known (56, 56+52, s)-Nets in Base 3

Best Known (56, 56+52, s)-Nets in Base 3

(56, 56+52, 56)-Net over F₃ — Constructive and digital

Digital (56, 108, 56)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 41, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 67, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(56, 56+52, 67)-Net over F₃ — Digital

Digital (56, 108, 67)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+52, 481)-Net in Base 3 — Upper bound on s

There is no (56, 108, 482)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3555 352054 719713 831358 038290 382006 008550 859312 765765 > 3¹⁰⁸ [i]