Best Known (105, 105+78, s)-Nets in Base 2
(105, 105+78, 60)-Net over F2 — Constructive and digital
Digital (105, 183, 60)-net over F2, using
- 1 times m-reduction [i] based on digital (105, 184, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 92, 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, 92, 30)-net over F4, using
(105, 105+78, 74)-Net over F2 — Digital
Digital (105, 183, 74)-net over F2, using
(105, 105+78, 297)-Net in Base 2 — Upper bound on s
There is no (105, 183, 298)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2183, 298, S2, 78), but
- 1 times code embedding in larger space [i] would yield OA(2184, 299, S2, 78), but
- adding a parity check bit [i] would yield OA(2185, 300, S2, 79), but
- the linear programming bound shows that M ≥ 141567 108182 629161 298008 913795 645564 742059 458353 673336 771152 211645 355218 507110 019263 646714 332578 792395 869231 595182 307914 419827 387939 160064 / 1898 352509 614315 308497 056354 652811 989510 912931 797163 098992 061786 535651 328793 485695 > 2185 [i]
- adding a parity check bit [i] would yield OA(2185, 300, S2, 79), but
- 1 times code embedding in larger space [i] would yield OA(2184, 299, S2, 78), but