Best Known (84, 171, s)-Nets in Base 8
(84, 171, 130)-Net over F8 — Constructive and digital
Digital (84, 171, 130)-net over F8, using
- t-expansion [i] based on digital (76, 171, 130)-net over F8, using
- 1 times m-reduction [i] based on digital (76, 172, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 62, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (14, 110, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 62, 65)-net over F8, using
- (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (76, 172, 130)-net over F8, using
(84, 171, 225)-Net in Base 8 — Constructive
(84, 171, 225)-net in base 8, using
- t-expansion [i] based on (83, 171, 225)-net in base 8, using
- 1 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
- 1 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
(84, 171, 255)-Net over F8 — Digital
Digital (84, 171, 255)-net over F8, using
(84, 171, 8941)-Net in Base 8 — Upper bound on s
There is no (84, 171, 8942)-net in base 8, because
- 1 times m-reduction [i] would yield (84, 170, 8942)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3359 754122 383225 678926 572898 630627 678815 635585 083725 479492 762000 587349 968411 145770 438067 829895 694961 161604 915558 174312 481605 064169 787878 383306 965950 125990 > 8170 [i]