Best Known (30, 117, s)-Nets in Base 8
(30, 117, 65)-Net over F8 — Constructive and digital
Digital (30, 117, 65)-net over F8, using
- t-expansion [i] based on digital (14, 117, 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
(30, 117, 97)-Net over F8 — Digital
Digital (30, 117, 97)-net over F8, using
- t-expansion [i] based on digital (28, 117, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(30, 117, 631)-Net in Base 8 — Upper bound on s
There is no (30, 117, 632)-net in base 8, because
- 1 times m-reduction [i] would yield (30, 116, 632)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 581 699865 733020 650252 050128 231384 903769 119031 947530 927499 712041 153514 032585 771605 868272 641657 327760 281698 > 8116 [i]