MinT - Best Known (138, 138+57, s)-Nets in Base 3

Best Known (138, 138+57, s)-Nets in Base 3

(138, 138+57, 252)-Net over F₃ — Constructive and digital

Digital (138, 195, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 65, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(138, 138+57, 472)-Net over F₃ — Digital

Digital (138, 195, 472)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+57, 11394)-Net in Base 3 — Upper bound on s

There is no (138, 195, 11395)-net in base 3, because

1 times m-reduction [i] would yield (138, 194, 11395)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 739082 605672 626623 887298 201648 324724 382733 993875 225109 787533 850402 700002 978704 084785 535273 > 3¹⁹⁴ [i]