MinT - Best Known (137, 137+55, s)-Nets in Base 3

Best Known (137, 137+55, s)-Nets in Base 3

(137, 137+55, 264)-Net over F₃ — Constructive and digital

Digital (137, 192, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 64, 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]

(137, 137+55, 498)-Net over F₃ — Digital

Digital (137, 192, 498)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+55, 12932)-Net in Base 3 — Upper bound on s

There is no (137, 192, 12933)-net in base 3, because

1 times m-reduction [i] would yield (137, 191, 12933)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 511054 957599 368354 762521 885924 768235 401563 048385 210471 054151 806304 983452 705792 791364 170059 > 3¹⁹¹ [i]