MinT - Best Known (132, 132+71, s)-Nets in Base 3

Best Known (132, 132+71, s)-Nets in Base 3

(132, 132+71, 156)-Net over F₃ — Constructive and digital

Digital (132, 203, 156)-net over F₃, using

17 times m-reduction [i] based on digital (132, 220, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 110, 78)-net over F₉, using
  - net from sequence [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]

(132, 132+71, 279)-Net over F₃ — Digital

Digital (132, 203, 279)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+71, 3909)-Net in Base 3 — Upper bound on s

There is no (132, 203, 3910)-net in base 3, because

1 times m-reduction [i] would yield (132, 202, 3910)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 404653 014743 759944 136327 382306 426116 829316 948775 374105 209385 677635 234171 602077 189295 022434 909345 > 3²⁰² [i]