Best Known (248−72, 248, s)-Nets in Base 2
(248−72, 248, 138)-Net over F2 — Constructive and digital
Digital (176, 248, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (176, 249, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 83, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 83, 46)-net over F8, using
(248−72, 248, 232)-Net over F2 — Digital
Digital (176, 248, 232)-net over F2, using
(248−72, 248, 1639)-Net in Base 2 — Upper bound on s
There is no (176, 248, 1640)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 455 719873 148874 532639 430294 627696 513782 467523 283894 592903 491239 985321 030141 > 2248 [i]