Best Known (145−114, 145, s)-Nets in Base 9
(145−114, 145, 78)-Net over F9 — Constructive and digital
Digital (31, 145, 78)-net over F9, using
- t-expansion [i] based on digital (22, 145, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(145−114, 145, 120)-Net over F9 — Digital
Digital (31, 145, 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
(145−114, 145, 703)-Net in Base 9 — Upper bound on s
There is no (31, 145, 704)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 340401 439836 745914 722904 141235 305217 254525 854610 924623 919553 364822 543938 101212 608792 135160 003208 917991 979818 936833 481794 932372 154931 316225 > 9145 [i]