Best Known (42, 42+74, s)-Nets in Base 8
(42, 42+74, 98)-Net over F8 — Constructive and digital
Digital (42, 116, 98)-net over F8, using
- t-expansion [i] based on digital (37, 116, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
(42, 42+74, 129)-Net over F8 — Digital
Digital (42, 116, 129)-net over F8, using
- t-expansion [i] based on digital (38, 116, 129)-net over F8, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 38 and N(F) ≥ 129, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
(42, 42+74, 1396)-Net in Base 8 — Upper bound on s
There is no (42, 116, 1397)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 584 091429 975824 211948 318287 046356 464685 897835 901777 966077 093757 916425 988247 635550 740309 887558 751702 246328 > 8116 [i]