Best Known (38, 38+81, s)-Nets in Base 16
(38, 38+81, 65)-Net over F16 — Constructive and digital
Digital (38, 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
(38, 38+81, 120)-Net in Base 16 — Constructive
(38, 119, 120)-net in base 16, using
- t-expansion [i] based on (37, 119, 120)-net in base 16, using
- 11 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- 11 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
(38, 38+81, 208)-Net over F16 — Digital
Digital (38, 119, 208)-net over F16, using
- t-expansion [i] based on digital (37, 119, 208)-net over F16, using
- net from sequence [i] based on digital (37, 207)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 37 and N(F) ≥ 208, using
- net from sequence [i] based on digital (37, 207)-sequence over F16, using
(38, 38+81, 3726)-Net in Base 16 — Upper bound on s
There is no (38, 119, 3727)-net in base 16, because
- 1 times m-reduction [i] would yield (38, 118, 3727)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 12281 305871 985970 662280 771516 889017 297401 839236 398141 584243 371362 135590 601789 528660 269798 612358 250746 457629 530110 531357 214724 589879 675774 077076 > 16118 [i]