MinT - Best Known (153−45, 153, s)-Nets in Base 3

Best Known (153−45, 153, s)-Nets in Base 3

(153−45, 153, 228)-Net over F₃ — Constructive and digital

Digital (108, 153, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 51, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(153−45, 153, 377)-Net over F₃ — Digital

Digital (108, 153, 377)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−45, 153, 8938)-Net in Base 3 — Upper bound on s

There is no (108, 153, 8939)-net in base 3, because

1 times m-reduction [i] would yield (108, 152, 8939)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 335644 069983 611430 313089 674652 375163 118088 872288 263142 722144 425755 054733 > 3¹⁵² [i]