Best Known (19, 19+32, s)-Nets in Base 8
(19, 19+32, 65)-Net over F8 — Constructive and digital
Digital (19, 51, 65)-net over F8, using
- t-expansion [i] based on digital (14, 51, 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
(19, 19+32, 724)-Net in Base 8 — Upper bound on s
There is no (19, 51, 725)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 11458 649157 490112 858025 388857 335442 905111 245761 > 851 [i]