MinT - Best Known (132, 132+105, s)-Nets in Base 3

Best Known (132, 132+105, s)-Nets in Base 3

(132, 132+105, 128)-Net over F₃ — Constructive and digital

Digital (132, 237, 128)-net over F₃, using

1 times m-reduction [i] based on digital (132, 238, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 119, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(132, 132+105, 163)-Net over F₃ — Digital

Digital (132, 237, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+105, 1429)-Net in Base 3 — Upper bound on s

There is no (132, 237, 1430)-net in base 3, because

1 times m-reduction [i] would yield (132, 236, 1430)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40946 837785 028449 684752 276404 600925 819223 653965 801604 300880 843914 365197 902307 641522 253051 181911 664711 188383 532777 > 3²³⁶ [i]