Best Known (123−49, 123, s)-Nets in Base 2
(123−49, 123, 56)-Net over F2 — Constructive and digital
Digital (74, 123, 56)-net over F2, using
- 1 times m-reduction [i] based on digital (74, 124, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 62, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- trace code for nets [i] based on digital (12, 62, 28)-net over F4, using
(123−49, 123, 63)-Net over F2 — Digital
Digital (74, 123, 63)-net over F2, using
(123−49, 123, 298)-Net in Base 2 — Upper bound on s
There is no (74, 123, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (74, 122, 299)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5 518944 643327 473399 415752 126865 363882 > 2122 [i]