Best Known (219−104, 219, s)-Nets in Base 2
(219−104, 219, 57)-Net over F2 — Constructive and digital
Digital (115, 219, 57)-net over F2, using
- t-expansion [i] based on digital (110, 219, 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
(219−104, 219, 73)-Net over F2 — Digital
Digital (115, 219, 73)-net over F2, using
- t-expansion [i] based on digital (114, 219, 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
(219−104, 219, 244)-Net in Base 2 — Upper bound on s
There is no (115, 219, 245)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2219, 245, S2, 104), but
- the linear programming bound shows that M ≥ 4341 942115 300131 305544 557532 316409 359084 249150 486924 502348 546498 754871 558144 / 4286 038185 > 2219 [i]