Best Known (142−71, 142, s)-Nets in Base 9
(142−71, 142, 165)-Net over F9 — Constructive and digital
Digital (71, 142, 165)-net over F9, using
- t-expansion [i] based on digital (64, 142, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(142−71, 142, 264)-Net over F9 — Digital
Digital (71, 142, 264)-net over F9, using
(142−71, 142, 12123)-Net in Base 9 — Upper bound on s
There is no (71, 142, 12124)-net in base 9, because
- 1 times m-reduction [i] would yield (71, 141, 12124)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 353 415448 791246 166052 501499 080748 342488 678934 468785 768071 724275 226895 449860 029342 059393 809009 143828 822922 006708 973661 719536 635479 156001 > 9141 [i]