MinT - Best Known (129, 246, s)-Nets in Base 3

Best Known (129, 246, s)-Nets in Base 3

(129, 246, 84)-Net over F₃ — Constructive and digital

Digital (129, 246, 84)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 84, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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 (45, 162, 48)-net over F₃, using
  - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
      - an explicitly constructive algebraic function field [i]

(129, 246, 138)-Net over F₃ — Digital

Digital (129, 246, 138)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 246, 1106)-Net in Base 3 — Upper bound on s

There is no (129, 246, 1107)-net in base 3, because

1 times m-reduction [i] would yield (129, 245, 1107)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 793 770132 154564 564260 961459 604144 334656 970485 438368 967302 174875 154843 204849 293185 651340 775334 833334 355489 582876 044565 > 3²⁴⁵ [i]