Best Known (4, 4+11, s)-Nets in Base 81
(4, 4+11, 150)-Net over F81 — Constructive and digital
Digital (4, 15, 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+11, 154)-Net over F81 — Digital
Digital (4, 15, 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+11, 7184)-Net in Base 81 — Upper bound on s
There is no (4, 15, 7185)-net in base 81, because
- 1 times m-reduction [i] would yield (4, 14, 7185)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 523 631481 917767 234159 994001 > 8114 [i]