Best Known (139−113, 139, s)-Nets in Base 9
(139−113, 139, 78)-Net over F9 — Constructive and digital
Digital (26, 139, 78)-net over F9, using
- t-expansion [i] based on digital (22, 139, 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
(139−113, 139, 110)-Net over F9 — Digital
Digital (26, 139, 110)-net over F9, using
- net from sequence [i] based on digital (26, 109)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 26 and N(F) ≥ 110, using
(139−113, 139, 575)-Net in Base 9 — Upper bound on s
There is no (26, 139, 576)-net in base 9, because
- 1 times m-reduction [i] would yield (26, 138, 576)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 498171 472405 139571 311081 310640 793044 751542 402594 840577 231004 851738 401081 252669 548671 561398 576126 553186 911671 527835 675117 473848 561665 > 9138 [i]