MinT - Best Known (189−59, 189, s)-Nets in Base 3

Best Known (189−59, 189, s)-Nets in Base 3

(189−59, 189, 192)-Net over F₃ — Constructive and digital

Digital (130, 189, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 63, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(189−59, 189, 372)-Net over F₃ — Digital

Digital (130, 189, 372)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−59, 189, 7201)-Net in Base 3 — Upper bound on s

There is no (130, 189, 7202)-net in base 3, because

1 times m-reduction [i] would yield (130, 188, 7202)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 500185 423272 135382 273102 310926 441660 083865 575915 041208 650519 364488 718940 424158 245134 382573 > 3¹⁸⁸ [i]