Best Known (207−90, 207, s)-Nets in Base 2
(207−90, 207, 60)-Net over F2 — Constructive and digital
Digital (117, 207, 60)-net over F2, using
- 1 times m-reduction [i] based on digital (117, 208, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 104, 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
- trace code for nets [i] based on digital (13, 104, 30)-net over F4, using
(207−90, 207, 79)-Net over F2 — Digital
Digital (117, 207, 79)-net over F2, using
(207−90, 207, 297)-Net in Base 2 — Upper bound on s
There is no (117, 207, 298)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2207, 298, S2, 90), but
- 1 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
- 1 times code embedding in larger space [i] would yield OA(2208, 299, S2, 90), but