Best Known (87, 87+128, s)-Nets in Base 2
(87, 87+128, 52)-Net over F2 — Constructive and digital
Digital (87, 215, 52)-net over F2, using
- t-expansion [i] based on digital (85, 215, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 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 (85, 51)-sequence over F2, using
(87, 87+128, 57)-Net over F2 — Digital
Digital (87, 215, 57)-net over F2, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(87, 87+128, 171)-Net in Base 2 — Upper bound on s
There is no (87, 215, 172)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 60493 634967 989141 979977 419881 810551 267955 026885 635774 596370 219074 > 2215 [i]