Best Known (78−41, 78, s)-Nets in Base 8
(78−41, 78, 98)-Net over F8 — Constructive and digital
Digital (37, 78, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(78−41, 78, 121)-Net over F8 — Digital
Digital (37, 78, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(78−41, 78, 3544)-Net in Base 8 — Upper bound on s
There is no (37, 78, 3545)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 77, 3545)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3454 243102 302242 915046 022742 138774 967992 001641 372876 321732 459849 137658 > 877 [i]