Best Known (198−123, 198, s)-Nets in Base 2
(198−123, 198, 50)-Net over F2 — Constructive and digital
Digital (75, 198, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(198−123, 198, 144)-Net in Base 2 — Upper bound on s
There is no (75, 198, 145)-net in base 2, because
- 1 times m-reduction [i] would yield (75, 197, 145)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 260475 329296 380373 936080 030785 009850 988728 926856 466162 026176 > 2197 [i]