Best Known (128−96, 128, s)-Nets in Base 9
(128−96, 128, 81)-Net over F9 — Constructive and digital
Digital (32, 128, 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
(128−96, 128, 120)-Net over F9 — Digital
Digital (32, 128, 120)-net over F9, using
- t-expansion [i] based on digital (31, 128, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
(128−96, 128, 791)-Net in Base 9 — Upper bound on s
There is no (32, 128, 792)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 140 545322 083754 260949 949665 907415 374343 092653 095123 893646 738093 906627 433560 709173 975683 361744 686189 242548 849881 455660 407809 > 9128 [i]