Best Known (114−71, 114, s)-Nets in Base 9
(114−71, 114, 81)-Net over F9 — Constructive and digital
Digital (43, 114, 81)-net over F9, using
- t-expansion [i] based on digital (32, 114, 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
(114−71, 114, 147)-Net over F9 — Digital
Digital (43, 114, 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
(114−71, 114, 2072)-Net in Base 9 — Upper bound on s
There is no (43, 114, 2073)-net in base 9, because
- 1 times m-reduction [i] would yield (43, 113, 2073)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 676639 990555 018205 538759 274348 171561 352238 716970 869907 966624 389119 834939 885563 057863 284363 108667 847477 013785 > 9113 [i]