Best Known (10, 10+109, s)-Nets in Base 16
(10, 10+109, 65)-Net over F16 — Constructive and digital
Digital (10, 119, 65)-net over F16, using
- t-expansion [i] based on digital (6, 119, 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
(10, 10+109, 81)-Net over F16 — Digital
Digital (10, 119, 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
(10, 10+109, 296)-Net in Base 16 — Upper bound on s
There is no (10, 119, 297)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16119, 297, S16, 109), but
- the linear programming bound shows that M ≥ 2035 412288 423101 062208 242858 095619 543141 495903 363849 525540 324349 490403 061338 238062 111579 976203 244404 236077 705749 186358 059817 088976 344414 419814 273899 517130 211426 801563 693772 035730 921525 749742 655160 141809 550770 974333 069358 484966 594450 057229 426773 270988 911180 932725 603119 640483 842165 309440 / 10307 501107 950381 867928 675101 099031 289182 510180 437080 402944 005394 928874 076611 071608 715962 220073 252363 990873 951071 809652 584141 089822 359641 881929 > 16119 [i]