Best Known (127−70, 127, s)-Nets in Base 9
(127−70, 127, 106)-Net over F9 — Constructive and digital
Digital (57, 127, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 40, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (17, 87, 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 (5, 40, 32)-net over F9, using
(127−70, 127, 182)-Net over F9 — Digital
Digital (57, 127, 182)-net over F9, using
- t-expansion [i] based on digital (50, 127, 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
(127−70, 127, 5021)-Net in Base 9 — Upper bound on s
There is no (57, 127, 5022)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15 455415 952058 781549 344635 180208 163925 669864 986364 557474 153068 822408 448373 342425 956791 808567 678186 368322 802071 405640 578449 > 9127 [i]