Best Known (28, 79, s)-Nets in Base 9
(28, 79, 78)-Net over F9 — Constructive and digital
Digital (28, 79, 78)-net over F9, using
- t-expansion [i] based on digital (22, 79, 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
(28, 79, 110)-Net over F9 — Digital
Digital (28, 79, 110)-net over F9, using
- t-expansion [i] based on digital (26, 79, 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
- net from sequence [i] based on digital (26, 109)-sequence over F9, using
(28, 79, 1192)-Net in Base 9 — Upper bound on s
There is no (28, 79, 1193)-net in base 9, because
- 1 times m-reduction [i] would yield (28, 78, 1193)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 274 723605 362242 229498 949585 292671 538390 177841 947063 435939 422875 542066 158345 > 978 [i]