Best Known (78−68, 78, s)-Nets in Base 81
(78−68, 78, 172)-Net over F81 — Constructive and digital
Digital (10, 78, 172)-net over F81, using
- t-expansion [i] based on digital (7, 78, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(78−68, 78, 244)-Net over F81 — Digital
Digital (10, 78, 244)-net over F81, using
- t-expansion [i] based on digital (9, 78, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(78−68, 78, 4025)-Net in Base 81 — Upper bound on s
There is no (10, 78, 4026)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 72861 543307 757380 498557 264166 890039 238476 531851 540387 434727 908317 010167 818266 757640 743825 446464 182277 159615 985626 169649 841865 225974 511365 311422 349121 > 8178 [i]