Best Known (247−144, 247, s)-Nets in Base 2
(247−144, 247, 55)-Net over F2 — Constructive and digital
Digital (103, 247, 55)-net over F2, using
- t-expansion [i] based on digital (100, 247, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(247−144, 247, 65)-Net over F2 — Digital
Digital (103, 247, 65)-net over F2, using
- t-expansion [i] based on digital (95, 247, 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
(247−144, 247, 205)-Net in Base 2 — Upper bound on s
There is no (103, 247, 206)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 264 195037 656681 551542 828087 503611 612558 895977 161723 131925 088015 997197 259433 > 2247 [i]