Best Known (79, 198, s)-Nets in Base 2
(79, 198, 50)-Net over F2 — Constructive and digital
Digital (79, 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
(79, 198, 52)-Net over F2 — Digital
Digital (79, 198, 52)-net over F2, using
- t-expansion [i] based on digital (77, 198, 52)-net over F2, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 77 and N(F) ≥ 52, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
(79, 198, 155)-Net in Base 2 — Upper bound on s
There is no (79, 198, 156)-net in base 2, because
- 1 times m-reduction [i] would yield (79, 197, 156)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 217410 887953 425788 291118 503502 174795 190961 198028 669411 949964 > 2197 [i]