MinT - Best Known (157−140, 157, s)-Nets in Base 3

Best Known (157−140, 157, s)-Nets in Base 3

(157−140, 157, 28)-Net over F₃ — Constructive and digital

Digital (17, 157, 28)-net over F₃, using

t-expansion [i] based on digital (15, 157, 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]

(157−140, 157, 44)-Net in Base 3 — Upper bound on s

There is no (17, 157, 45)-net in base 3, because

27 times m-reduction [i] would yield (17, 130, 45)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹³⁰, 45, S₃, 3, 113), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2865 014852 390475 710679 572105 323242 035759 805416 923029 389510 561523 / 19 > 3¹³⁰ [i]