MinT - Best Known (132, 132+51, s)-Nets in Base 3

Best Known (132, 132+51, s)-Nets in Base 3

(132, 132+51, 282)-Net over F₃ — Constructive and digital

Digital (132, 183, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 61, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(132, 132+51, 526)-Net over F₃ — Digital

Digital (132, 183, 526)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+51, 15112)-Net in Base 3 — Upper bound on s

There is no (132, 183, 15113)-net in base 3, because

1 times m-reduction [i] would yield (132, 182, 15113)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 686 192922 481705 828909 464350 344628 825799 133137 467330 943535 101150 823512 157519 640220 737331 > 3¹⁸² [i]