Best Known (9, 9+100, s)-Nets in Base 16
(9, 9+100, 65)-Net over F16 — Constructive and digital
Digital (9, 109, 65)-net over F16, using
- t-expansion [i] based on digital (6, 109, 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
(9, 9+100, 72)-Net over F16 — Digital
Digital (9, 109, 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
(9, 9+100, 272)-Net in Base 16 — Upper bound on s
There is no (9, 109, 273)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16109, 273, S16, 100), but
- the linear programming bound shows that M ≥ 273 657358 512371 984993 519372 551189 865511 839531 294522 571665 736760 007129 977261 413471 314074 433953 259003 124596 070788 023890 112521 347074 261847 286473 416611 340983 241051 015715 954340 677689 631342 723094 271996 740005 764207 013701 269035 557599 657476 883212 140544 / 1519 190122 992982 546151 946187 449503 756222 421172 231169 179174 056802 951286 153357 234619 606733 506299 494217 290307 575649 > 16109 [i]