Best Known (17, 36, s)-Nets in Base 16
(17, 36, 98)-Net over F16 — Constructive and digital
Digital (17, 36, 98)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (6, 25, 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
- digital (2, 11, 33)-net over F16, using
(17, 36, 137)-Net over F16 — Digital
Digital (17, 36, 137)-net over F16, using
(17, 36, 150)-Net in Base 16 — Constructive
(17, 36, 150)-net in base 16, using
- 161 times duplication [i] based on (16, 35, 150)-net in base 16, using
- base change [i] based on digital (1, 20, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 20, 150)-net over F128, using
(17, 36, 13310)-Net in Base 16 — Upper bound on s
There is no (17, 36, 13311)-net in base 16, because
- 1 times m-reduction [i] would yield (17, 35, 13311)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 394135 008979 647738 483450 449374 723793 342586 > 1635 [i]