MinT - Best Known (125−109, 125, s)-Nets in Base 3

Best Known (125−109, 125, s)-Nets in Base 3

(125−109, 125, 28)-Net over F₃ — Constructive and digital

Digital (16, 125, 28)-net over F₃, using

t-expansion [i] based on digital (15, 125, 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]

(125−109, 125, 42)-Net in Base 3 — Upper bound on s

There is no (16, 125, 43)-net in base 3, because

2 times m-reduction [i] would yield (16, 123, 43)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹²³, 43, S₃, 3, 107), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 52113 298697 518505 101982 215055 778546 152212 793198 597682 085629 > 3¹²³ [i]