Best Known (125−115, 125, s)-Nets in Base 16
(125−115, 125, 65)-Net over F16 — Constructive and digital
Digital (10, 125, 65)-net over F16, using
- t-expansion [i] based on digital (6, 125, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(125−115, 125, 81)-Net over F16 — Digital
Digital (10, 125, 81)-net over F16, using
- net from sequence [i] based on digital (10, 80)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 10 and N(F) ≥ 81, using
(125−115, 125, 293)-Net in Base 16 — Upper bound on s
There is no (10, 125, 294)-net in base 16, because
- 5 times m-reduction [i] would yield (10, 120, 294)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16120, 294, S16, 110), but
- the linear programming bound shows that M ≥ 5163 898339 652977 786117 801946 121924 548638 356257 979360 212828 869792 290428 169649 144926 580550 976405 400680 227334 299534 218149 119609 129276 655870 587113 147038 314409 102414 676543 979952 268114 925477 342940 325104 332606 409819 280529 357514 664198 260814 651116 032492 483643 026939 787622 447303 775848 759296 / 1587 889732 247706 487992 888575 018143 166022 150661 383580 402154 689523 294369 559832 402766 791037 688773 365164 605925 357895 205261 149093 489594 946891 > 16120 [i]
- extracting embedded orthogonal array [i] would yield OA(16120, 294, S16, 110), but