Best Known (84, 84+78, s)-Nets in Base 8
(84, 84+78, 208)-Net over F8 — Constructive and digital
Digital (84, 162, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 81, 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
(84, 84+78, 225)-Net in Base 8 — Constructive
(84, 162, 225)-net in base 8, using
- t-expansion [i] based on (83, 162, 225)-net in base 8, using
- 10 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
- 10 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
(84, 84+78, 304)-Net over F8 — Digital
Digital (84, 162, 304)-net over F8, using
(84, 84+78, 12381)-Net in Base 8 — Upper bound on s
There is no (84, 162, 12382)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 200 280030 677551 748202 229031 461324 939818 656767 175139 818718 448681 593687 512990 798569 067086 917385 910998 830456 953582 386120 592433 092252 056879 152042 942696 > 8162 [i]