Best Known (114−105, 114, s)-Nets in Base 16
(114−105, 114, 65)-Net over F16 — Constructive and digital
Digital (9, 114, 65)-net over F16, using
- t-expansion [i] based on digital (6, 114, 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
(114−105, 114, 72)-Net over F16 — Digital
Digital (9, 114, 72)-net over F16, using
- net from sequence [i] based on digital (9, 71)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
(114−105, 114, 251)-Net in Base 16 — Upper bound on s
There is no (9, 114, 252)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16114, 252, S16, 105), but
- the linear programming bound shows that M ≥ 2 748790 826596 963742 189244 658598 251650 175072 752552 398307 518925 252579 746294 633879 787752 424454 713609 645217 184843 232896 028777 776559 145490 457677 225343 856836 404174 310532 023170 486350 939514 926172 170676 682269 993084 452434 418574 993913 228243 772986 209555 794272 016681 729053 949952 / 14 276119 542823 434554 057648 278984 401837 130051 095626 470058 076655 320850 299262 974348 103465 540493 125958 754090 697689 697269 194130 785327 > 16114 [i]