Best Known (56, 56+88, s)-Nets in Base 9
(56, 56+88, 81)-Net over F9 — Constructive and digital
Digital (56, 144, 81)-net over F9, using
- t-expansion [i] based on digital (32, 144, 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
(56, 56+88, 84)-Net in Base 9 — Constructive
(56, 144, 84)-net in base 9, using
- base change [i] based on digital (8, 96, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(56, 56+88, 182)-Net over F9 — Digital
Digital (56, 144, 182)-net over F9, using
- t-expansion [i] based on digital (50, 144, 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
(56, 56+88, 2835)-Net in Base 9 — Upper bound on s
There is no (56, 144, 2836)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 257633 991201 048644 559339 562155 169429 632909 534416 054183 529380 857390 194452 435838 295198 527563 440583 352840 975744 289624 760218 635303 628072 283265 > 9144 [i]