Best Known (106−74, 106, s)-Nets in Base 9
(106−74, 106, 81)-Net over F9 — Constructive and digital
Digital (32, 106, 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
(106−74, 106, 120)-Net over F9 — Digital
Digital (32, 106, 120)-net over F9, using
- t-expansion [i] based on digital (31, 106, 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
(106−74, 106, 969)-Net in Base 9 — Upper bound on s
There is no (32, 106, 970)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 142629 657969 646748 058837 403730 803369 891771 830257 875097 002023 974247 987157 390513 245772 631322 048996 030225 > 9106 [i]