MinT - Best Known (123, 123+120, s)-Nets in Base 3

Best Known (123, 123+120, s)-Nets in Base 3

(123, 123+120, 78)-Net over F₃ — Constructive and digital

Digital (123, 243, 78)-net over F₃, using

t-expansion [i] based on digital (121, 243, 78)-net over F₃, using
- net from sequence [i] based on digital (121, 77)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(123, 123+120, 123)-Net over F₃ — Digital

Digital (123, 243, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+120, 934)-Net in Base 3 — Upper bound on s

There is no (123, 243, 935)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91 240953 824427 145533 684606 991965 332041 709449 584909 311496 013136 687227 401816 060820 373795 438670 583407 664229 031937 665417 > 3²⁴³ [i]