Best Known (222−106, 222, s)-Nets in Base 2
(222−106, 222, 57)-Net over F2 — Constructive and digital
Digital (116, 222, 57)-net over F2, using
- t-expansion [i] based on digital (110, 222, 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
(222−106, 222, 73)-Net over F2 — Digital
Digital (116, 222, 73)-net over F2, using
- t-expansion [i] based on digital (114, 222, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(222−106, 222, 246)-Net in Base 2 — Upper bound on s
There is no (116, 222, 247)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2222, 247, S2, 106), but
- the linear programming bound shows that M ≥ 84288 764360 551408 231018 394746 066484 986436 989913 374059 111409 815037 315395 878912 / 9835 737417 > 2222 [i]