Best Known (35−23, 35, s)-Nets in Base 16
(35−23, 35, 65)-Net over F16 — Constructive and digital
Digital (12, 35, 65)-net over F16, using
- t-expansion [i] based on digital (6, 35, 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
(35−23, 35, 76)-Net in Base 16 — Constructive
(12, 35, 76)-net in base 16, using
- base change [i] based on digital (5, 28, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
(35−23, 35, 88)-Net over F16 — Digital
Digital (12, 35, 88)-net over F16, using
- net from sequence [i] based on digital (12, 87)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 12 and N(F) ≥ 88, using
(35−23, 35, 1719)-Net in Base 16 — Upper bound on s
There is no (12, 35, 1720)-net in base 16, because
- 1 times m-reduction [i] would yield (12, 34, 1720)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 87608 130966 409246 976397 959697 373246 391926 > 1634 [i]