Best Known (4, 4+37, s)-Nets in Base 81
(4, 4+37, 150)-Net over F81 — Constructive and digital
Digital (4, 41, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
(4, 4+37, 154)-Net over F81 — Digital
Digital (4, 41, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
(4, 4+37, 1636)-Net in Base 81 — Upper bound on s
There is no (4, 41, 1637)-net in base 81, because
- 1 times m-reduction [i] would yield (4, 40, 1637)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 22063 028539 405055 004279 305715 860546 398808 253030 373496 911149 349794 386290 222881 > 8140 [i]