Best Known (30, 30+138, s)-Nets in Base 8
(30, 30+138, 65)-Net over F8 — Constructive and digital
Digital (30, 168, 65)-net over F8, using
- t-expansion [i] based on digital (14, 168, 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, 30+138, 97)-Net over F8 — Digital
Digital (30, 168, 97)-net over F8, using
- t-expansion [i] based on digital (28, 168, 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, 30+138, 556)-Net in Base 8 — Upper bound on s
There is no (30, 168, 557)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 58 443534 962900 252429 582772 454358 443961 810592 590961 245838 282600 019169 821896 560680 091818 711887 687013 566635 048171 289835 396715 154501 659272 086416 634538 516224 > 8168 [i]