Best Known (227−106, 227, s)-Nets in Base 2
(227−106, 227, 57)-Net over F2 — Constructive and digital
Digital (121, 227, 57)-net over F2, using
- t-expansion [i] based on digital (110, 227, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(227−106, 227, 80)-Net over F2 — Digital
Digital (121, 227, 80)-net over F2, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 121 and N(F) ≥ 80, using
(227−106, 227, 261)-Net in Base 2 — Upper bound on s
There is no (121, 227, 262)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2227, 262, S2, 106), but
- the linear programming bound shows that M ≥ 16461 326461 594735 615540 825227 700001 317871 050464 705619 012646 449971 407593 456091 004928 / 72 093764 583225 > 2227 [i]