Best Known (108, 108+80, s)-Nets in Base 2
(108, 108+80, 60)-Net over F2 — Constructive and digital
Digital (108, 188, 60)-net over F2, using
- 2 times m-reduction [i] based on digital (108, 190, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 95, 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, 95, 30)-net over F4, using
(108, 108+80, 76)-Net over F2 — Digital
Digital (108, 188, 76)-net over F2, using
(108, 108+80, 298)-Net in Base 2 — Upper bound on s
There is no (108, 188, 299)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2188, 299, S2, 80), but
- adding a parity check bit [i] would yield OA(2189, 300, S2, 81), but
- the linear programming bound shows that M ≥ 333112 132422 259965 088720 215000 611770 757764 145862 673192 223023 087630 748136 412561 549060 805697 390758 928463 024902 788757 444450 017971 109260 951552 / 284 805581 394495 166949 489186 936966 421059 043171 883994 793835 511370 537717 840519 721875 > 2189 [i]
- adding a parity check bit [i] would yield OA(2189, 300, S2, 81), but