MinT - Best Known (57−3, 57, s)-Nets in Base 3

Best Known (57−3, 57, s)-Nets in Base 3

(57−3, 57, large)-Net over F₃ — Constructive and digital

Digital (54, 57, large)-net over F₃, using

3²³ times duplication [i] based on digital (31, 34, large)-net over F₃, using
- t-expansion [i] based on digital (30, 34, large)-net over F₃, using
  - nets constructed from net-embeddable BCH codes [i]

(57−3, 57, large)-Net in Base 3 — Upper bound on s

There is no (54, 57, large)-net in base 3, because

1 times m-reduction [i] would yield (54, 56, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]