Best Known (111, 111+84, s)-Nets in Base 2
(111, 111+84, 60)-Net over F2 — Constructive and digital
Digital (111, 195, 60)-net over F2, using
- 1 times m-reduction [i] based on digital (111, 196, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 98, 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, 98, 30)-net over F4, using
(111, 111+84, 76)-Net over F2 — Digital
Digital (111, 195, 76)-net over F2, using
(111, 111+84, 297)-Net in Base 2 — Upper bound on s
There is no (111, 195, 298)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2195, 298, S2, 84), but
- 1 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- the linear programming bound shows that M ≥ 333445 596634 842101 957662 761369 966680 970228 955880 375209 681209 067512 159971 176505 925710 036206 046927 475988 200870 117376 / 1 055603 696799 631985 996897 950925 994087 362055 971326 408581 > 2197 [i]
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- 1 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but