Best Known (10, 58, s)-Nets in Base 16
(10, 58, 65)-Net over F16 — Constructive and digital
Digital (10, 58, 65)-net over F16, using
- t-expansion [i] based on digital (6, 58, 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, 58, 81)-Net over F16 — Digital
Digital (10, 58, 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, 58, 518)-Net in Base 16 — Upper bound on s
There is no (10, 58, 519)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7173 463997 885810 851598 888155 028650 091983 019179 654183 760483 344024 225216 > 1658 [i]