MinT - Best Known (132, 132+52, s)-Nets in Base 3

Best Known (132, 132+52, s)-Nets in Base 3

(132, 132+52, 264)-Net over F₃ — Constructive and digital

Digital (132, 184, 264)-net over F₃, using

3¹ times duplication [i] based on digital (131, 183, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 61, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(132, 132+52, 503)-Net over F₃ — Digital

Digital (132, 184, 503)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+52, 12529)-Net in Base 3 — Upper bound on s

There is no (132, 184, 12530)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6177 684580 859422 281563 143684 086126 495882 222530 642760 364185 387908 445870 617572 015759 705125 > 3¹⁸⁴ [i]