MinT - Best Known (166−51, 166, s)-Nets in Base 3

Best Known (166−51, 166, s)-Nets in Base 3

(166−51, 166, 192)-Net over F₃ — Constructive and digital

Digital (115, 166, 192)-net over F₃, using

3¹ times duplication [i] based on digital (114, 165, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 55, 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]

(166−51, 166, 350)-Net over F₃ — Digital

Digital (115, 166, 350)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−51, 166, 7146)-Net in Base 3 — Upper bound on s

There is no (115, 166, 7147)-net in base 3, because

1 times m-reduction [i] would yield (115, 165, 7147)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312529 985225 729975 871320 431622 612396 085701 408625 760035 149316 740891 322302 505703 > 3¹⁶⁵ [i]