Best Known (7, 106, s)-Nets in Base 16
(7, 106, 65)-Net over F16 — Constructive and digital
Digital (7, 106, 65)-net over F16, using
- t-expansion [i] based on digital (6, 106, 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
(7, 106, 148)-Net in Base 16 — Upper bound on s
There is no (7, 106, 149)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16106, 149, S16, 99), but
- the linear programming bound shows that M ≥ 816 599733 134915 060102 286791 014279 570961 808647 561259 701622 727972 318580 814468 586788 704719 888021 758511 180387 185497 294014 860169 599694 236569 956897 906459 680645 840896 / 18 611731 458664 877001 506461 273395 > 16106 [i]