Best Known (109, 109+82, s)-Nets in Base 2
(109, 109+82, 60)-Net over F2 — Constructive and digital
Digital (109, 191, 60)-net over F2, using
- 1 times m-reduction [i] based on digital (109, 192, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 96, 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, 96, 30)-net over F4, using
(109, 109+82, 76)-Net over F2 — Digital
Digital (109, 191, 76)-net over F2, using
(109, 109+82, 297)-Net in Base 2 — Upper bound on s
There is no (109, 191, 298)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2191, 298, S2, 82), but
- 1 times code embedding in larger space [i] would yield OA(2192, 299, S2, 82), but
- adding a parity check bit [i] would yield OA(2193, 300, S2, 83), but
- the linear programming bound shows that M ≥ 47301 037877 562348 126535 964476 521603 387556 508620 623293 070152 196591 060102 430290 310541 234357 121691 993687 546336 928736 477184 / 2 739614 630568 907331 852802 953012 407724 450650 903550 704398 106875 > 2193 [i]
- adding a parity check bit [i] would yield OA(2193, 300, S2, 83), but
- 1 times code embedding in larger space [i] would yield OA(2192, 299, S2, 82), but