Best Known (44, 44+88, s)-Nets in Base 9
(44, 44+88, 81)-Net over F9 — Constructive and digital
Digital (44, 132, 81)-net over F9, using
- t-expansion [i] based on digital (32, 132, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(44, 44+88, 147)-Net over F9 — Digital
Digital (44, 132, 147)-net over F9, using
- t-expansion [i] based on digital (43, 132, 147)-net over F9, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
(44, 44+88, 1545)-Net in Base 9 — Upper bound on s
There is no (44, 132, 1546)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 924240 258510 336272 289653 204923 137050 455908 372146 797742 221581 085123 042395 158183 828909 854625 619876 653380 754879 213671 909281 402177 > 9132 [i]