Best Known (17, 70, s)-Nets in Base 8
(17, 70, 65)-Net over F8 — Constructive and digital
Digital (17, 70, 65)-net over F8, using
- t-expansion [i] based on digital (14, 70, 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
(17, 70, 359)-Net in Base 8 — Upper bound on s
There is no (17, 70, 360)-net in base 8, because
- 1 times m-reduction [i] would yield (17, 69, 360)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 209 834380 120760 618642 841041 443233 194195 548087 576048 766616 897436 > 869 [i]