Best Known (255−150, 255, s)-Nets in Base 2
(255−150, 255, 56)-Net over F2 — Constructive and digital
Digital (105, 255, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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]
(255−150, 255, 65)-Net over F2 — Digital
Digital (105, 255, 65)-net over F2, using
- t-expansion [i] based on digital (95, 255, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(255−150, 255, 207)-Net in Base 2 — Upper bound on s
There is no (105, 255, 208)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 69580 482228 314172 836362 535261 689409 173712 783863 246830 000894 633938 929991 804773 > 2255 [i]