Best Known (198−122, 198, s)-Nets in Base 2
(198−122, 198, 50)-Net over F2 — Constructive and digital
Digital (76, 198, 50)-net over F2, using
- t-expansion [i] based on 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]
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
(198−122, 198, 146)-Net in Base 2 — Upper bound on s
There is no (76, 198, 147)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 464022 285925 253680 427462 901047 923030 563239 038879 444621 284352 > 2198 [i]