Best Known (88, 168, s)-Nets in Base 8
(88, 168, 208)-Net over F8 — Constructive and digital
Digital (88, 168, 208)-net over F8, using
- 2 times m-reduction [i] based on digital (88, 170, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 85, 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, 85, 104)-net over F64, using
(88, 168, 225)-Net in Base 8 — Constructive
(88, 168, 225)-net in base 8, using
- t-expansion [i] based on (83, 168, 225)-net in base 8, using
- 4 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
- base change [i] based on digital (40, 129, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- base change [i] based on digital (40, 129, 225)-net over F16, using
- 4 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
(88, 168, 329)-Net over F8 — Digital
Digital (88, 168, 329)-net over F8, using
(88, 168, 13960)-Net in Base 8 — Upper bound on s
There is no (88, 168, 13961)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 52 512952 213063 595863 598927 295881 730097 364715 313027 572499 582332 693181 789178 448066 340964 454652 543438 993948 674056 806761 996439 977573 981304 814692 918416 675804 > 8168 [i]