Best Known (116, 206, s)-Nets in Base 2
(116, 206, 60)-Net over F2 — Constructive and digital
Digital (116, 206, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 103, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
(116, 206, 77)-Net over F2 — Digital
Digital (116, 206, 77)-net over F2, using
(116, 206, 296)-Net in Base 2 — Upper bound on s
There is no (116, 206, 297)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2206, 297, S2, 90), but
- 2 times code embedding in larger space [i] would yield OA(2208, 299, S2, 90), but
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- the linear programming bound shows that M ≥ 437987 836379 661851 428112 482969 460104 960459 291237 979833 080590 515802 667419 590325 215760 903409 709975 863296 / 433 753365 263741 276278 643266 060465 678125 > 2209 [i]
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- 2 times code embedding in larger space [i] would yield OA(2208, 299, S2, 90), but