Best Known (79, 79+142, s)-Nets in Base 2
(79, 79+142, 50)-Net over F2 — Constructive and digital
Digital (79, 221, 50)-net over F2, using
- t-expansion [i] based on digital (75, 221, 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, 79+142, 52)-Net over F2 — Digital
Digital (79, 221, 52)-net over F2, using
- t-expansion [i] based on digital (77, 221, 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, 79+142, 147)-Net in Base 2 — Upper bound on s
There is no (79, 221, 148)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 931533 650890 445344 491143 072757 113937 349263 423724 927964 722192 776936 > 2221 [i]