Best Known (56−37, 56, s)-Nets in Base 8
(56−37, 56, 65)-Net over F8 — Constructive and digital
Digital (19, 56, 65)-net over F8, using
- t-expansion [i] based on digital (14, 56, 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
(56−37, 56, 609)-Net in Base 8 — Upper bound on s
There is no (19, 56, 610)-net in base 8, because
- 1 times m-reduction [i] would yield (19, 55, 610)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 47 995222 606232 077255 805428 602528 061242 179936 845616 > 855 [i]