Best Known (10, 10+16, s)-Nets in Base 16
(10, 10+16, 65)-Net over F16 — Constructive and digital
Digital (10, 26, 65)-net over F16, using
- t-expansion [i] based on digital (6, 26, 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
(10, 10+16, 80)-Net in Base 16 — Constructive
(10, 26, 80)-net in base 16, using
- 1 times m-reduction [i] based on (10, 27, 80)-net in base 16, using
- base change [i] based on digital (1, 18, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 18, 80)-net over F64, using
(10, 10+16, 81)-Net over F16 — Digital
Digital (10, 26, 81)-net over F16, using
- net from sequence [i] based on digital (10, 80)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 10 and N(F) ≥ 81, using
(10, 10+16, 2051)-Net in Base 16 — Upper bound on s
There is no (10, 26, 2052)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 20 297706 467217 244199 360926 518016 > 1626 [i]