Best Known (51, 51+62, s)-Nets in Base 9
(51, 51+62, 102)-Net over F9 — Constructive and digital
Digital (51, 113, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 34, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (17, 79, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (3, 34, 28)-net over F9, using
(51, 51+62, 182)-Net over F9 — Digital
Digital (51, 113, 182)-net over F9, using
- t-expansion [i] based on digital (50, 113, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(51, 51+62, 4651)-Net in Base 9 — Upper bound on s
There is no (51, 113, 4652)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 679279 474685 852035 832483 627840 776774 535839 751807 495969 654605 617133 223167 700057 676353 847945 438640 308194 288161 > 9113 [i]