Best Known (165, 165+40, s)-Nets in Base 4
(165, 165+40, 1539)-Net over F4 — Constructive and digital
Digital (165, 205, 1539)-net over F4, using
- 41 times duplication [i] based on digital (164, 204, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 68, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 68, 513)-net over F64, using
(165, 165+40, 7518)-Net over F4 — Digital
Digital (165, 205, 7518)-net over F4, using
(165, 165+40, 4104858)-Net in Base 4 — Upper bound on s
There is no (165, 205, 4104859)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2644 232044 916148 216193 971168 559431 534656 310539 907922 933503 610166 487893 412822 095139 738726 373233 671030 975057 286394 485465 475654 > 4205 [i]