Best Known (131−53, 131, s)-Nets in Base 2
(131−53, 131, 56)-Net over F2 — Constructive and digital
Digital (78, 131, 56)-net over F2, using
- 1 times m-reduction [i] based on digital (78, 132, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 66, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- trace code for nets [i] based on digital (12, 66, 28)-net over F4, using
(131−53, 131, 64)-Net over F2 — Digital
Digital (78, 131, 64)-net over F2, using
(131−53, 131, 298)-Net in Base 2 — Upper bound on s
There is no (78, 131, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (78, 130, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2130, 299, S2, 52), but
- adding a parity check bit [i] would yield OA(2131, 300, S2, 53), but
- the linear programming bound shows that M ≥ 835249 546947 854888 934372 794550 726415 005267 977549 831092 670722 083310 197796 074880 145116 734749 866628 024518 331713 335458 699168 606177 139658 705940 276891 242247 945827 850895 594922 967040 / 197 715390 170736 894872 721273 822471 708749 073790 701017 854820 620754 271824 242229 889302 199127 061206 521535 614768 633139 933238 769796 252031 306401 > 2131 [i]
- adding a parity check bit [i] would yield OA(2131, 300, S2, 53), but
- extracting embedded orthogonal array [i] would yield OA(2130, 299, S2, 52), but