Best Known (84−57, 84, s)-Nets in Base 8
(84−57, 84, 65)-Net over F8 — Constructive and digital
Digital (27, 84, 65)-net over F8, using
- t-expansion [i] based on digital (14, 84, 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
(84−57, 84, 96)-Net over F8 — Digital
Digital (27, 84, 96)-net over F8, using
- net from sequence [i] based on digital (27, 95)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 27 and N(F) ≥ 96, using
(84−57, 84, 749)-Net in Base 8 — Upper bound on s
There is no (27, 84, 750)-net in base 8, because
- 1 times m-reduction [i] would yield (27, 83, 750)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 909 639328 420866 115927 181335 584117 778573 119797 356200 943812 049616 804621 217086 > 883 [i]