MinT - Best Known (42−22, 42, s)-Nets in Base 3

Best Known (42−22, 42, s)-Nets in Base 3

(42−22, 42, 28)-Net over F₃ — Constructive and digital

Digital (20, 42, 28)-net over F₃, using

t-expansion [i] based on digital (15, 42, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(42−22, 42, 32)-Net over F₃ — Digital

Digital (20, 42, 32)-net over F₃, using

t-expansion [i] based on digital (19, 42, 32)-net over F₃, using
- net from sequence [i] based on digital (19, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 19 and N(F) ≥ 32, using
    - a curve from the manYPoints database [i]

(42−22, 42, 152)-Net in Base 3 — Upper bound on s

There is no (20, 42, 153)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 112 419373 308252 859163 > 3⁴² [i]