Best Known (173−47, 173, s)-Nets in Base 2
(173−47, 173, 138)-Net over F2 — Constructive and digital
Digital (126, 173, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (126, 174, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 58, 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, 58, 46)-net over F8, using
(173−47, 173, 201)-Net over F2 — Digital
Digital (126, 173, 201)-net over F2, using
(173−47, 173, 1647)-Net in Base 2 — Upper bound on s
There is no (126, 173, 1648)-net in base 2, because
- 1 times m-reduction [i] would yield (126, 172, 1648)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 6020 887781 073811 759675 758204 428450 250378 000292 930118 > 2172 [i]