MinT - Best Known (132−35, 132, s)-Nets in Base 3

Best Known (132−35, 132, s)-Nets in Base 3

(132−35, 132, 264)-Net over F₃ — Constructive and digital

Digital (97, 132, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 44, 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]

(132−35, 132, 488)-Net over F₃ — Digital

Digital (97, 132, 488)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−35, 132, 17026)-Net in Base 3 — Upper bound on s

There is no (97, 132, 17027)-net in base 3, because

1 times m-reduction [i] would yield (97, 131, 17027)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 318 374194 588118 042795 885860 383968 939816 484979 715830 433707 146087 > 3¹³¹ [i]