Best Known (83−37, 83, s)-Nets in Base 8
(83−37, 83, 208)-Net over F8 — Constructive and digital
Digital (46, 83, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (46, 86, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 43, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 43, 104)-net over F64, using
(83−37, 83, 258)-Net over F8 — Digital
Digital (46, 83, 258)-net over F8, using
- 1 times m-reduction [i] based on digital (46, 84, 258)-net over F8, using
- trace code for nets [i] based on digital (4, 42, 129)-net over F64, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- trace code for nets [i] based on digital (4, 42, 129)-net over F64, using
(83−37, 83, 14020)-Net in Base 8 — Upper bound on s
There is no (46, 83, 14021)-net in base 8, because
- 1 times m-reduction [i] would yield (46, 82, 14021)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 113 139521 054246 300780 377700 448484 017299 508403 818380 038058 280034 126041 134392 > 882 [i]