Best Known (215−132, 215, s)-Nets in Base 2
(215−132, 215, 51)-Net over F2 — Constructive and digital
Digital (83, 215, 51)-net over F2, using
- t-expansion [i] based on digital (80, 215, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 places 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 (80, 50)-sequence over F2, using
(215−132, 215, 57)-Net over F2 — Digital
Digital (83, 215, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
(215−132, 215, 159)-Net in Base 2 — Upper bound on s
There is no (83, 215, 160)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 58619 630990 108911 601802 865664 639625 842972 345597 435466 418013 747230 > 2215 [i]