Best Known (67−52, 67, s)-Nets in Base 81
(67−52, 67, 224)-Net over F81 — Constructive and digital
Digital (15, 67, 224)-net over F81, using
- t-expansion [i] based on digital (13, 67, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(67−52, 67, 298)-Net over F81 — Digital
Digital (15, 67, 298)-net over F81, using
- t-expansion [i] based on digital (12, 67, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(67−52, 67, 10907)-Net in Base 81 — Upper bound on s
There is no (15, 67, 10908)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 74 021729 292303 515418 260266 152769 068716 515873 813884 032935 356509 690393 418366 749751 610047 899126 615525 360357 326818 967148 423881 568641 > 8167 [i]