MinT - Best Known (89−53, 89, s)-Nets in Base 3

Best Known (89−53, 89, s)-Nets in Base 3

(89−53, 89, 38)-Net over F₃ — Constructive and digital

Digital (36, 89, 38)-net over F₃, using

t-expansion [i] based on digital (32, 89, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(89−53, 89, 48)-Net over F₃ — Digital

Digital (36, 89, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(89−53, 89, 193)-Net in Base 3 — Upper bound on s

There is no (36, 89, 194)-net in base 3, because

1 times m-reduction [i] would yield (36, 88, 194)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 091516 880355 772821 525141 340229 670668 850053 > 3⁸⁸ [i]