Best Known (177−75, 177, s)-Nets in Base 2
(177−75, 177, 60)-Net over F2 — Constructive and digital
Digital (102, 177, 60)-net over F2, using
- 1 times m-reduction [i] based on digital (102, 178, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 89, 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, 89, 30)-net over F4, using
(177−75, 177, 73)-Net over F2 — Digital
Digital (102, 177, 73)-net over F2, using
(177−75, 177, 298)-Net in Base 2 — Upper bound on s
There is no (102, 177, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (102, 176, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2176, 299, S2, 74), but
- adding a parity check bit [i] would yield OA(2177, 300, S2, 75), but
- the linear programming bound shows that M ≥ 3 635392 612138 849947 593748 250106 276323 244402 593086 652587 881083 736015 264809 747844 602393 772282 952895 309564 287520 927482 512784 061552 651238 260008 282439 847339 186197 936622 918149 603328 / 16 596489 288891 597431 806767 668273 879726 323125 162254 820959 724017 639569 206174 043207 555202 380507 742012 504078 557367 932811 307081 > 2177 [i]
- adding a parity check bit [i] would yield OA(2177, 300, S2, 75), but
- extracting embedded orthogonal array [i] would yield OA(2176, 299, S2, 74), but