Best Known (247−140, 247, s)-Nets in Base 2
(247−140, 247, 56)-Net over F2 — Constructive and digital
Digital (107, 247, 56)-net over F2, using
- t-expansion [i] based on digital (105, 247, 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]
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
(247−140, 247, 65)-Net over F2 — Digital
Digital (107, 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
(247−140, 247, 219)-Net in Base 2 — Upper bound on s
There is no (107, 247, 220)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 251 823773 123223 848603 879265 814850 793929 496262 637852 025811 656776 471540 307038 > 2247 [i]