Best Known (130, 130+83, s)-Nets in Base 3
(130, 130+83, 156)-Net over F3 — Constructive and digital
Digital (130, 213, 156)-net over F3, using
- 3 times m-reduction [i] based on digital (130, 216, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 108, 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
- trace code for nets [i] based on digital (22, 108, 78)-net over F9, using
(130, 130+83, 213)-Net over F3 — Digital
Digital (130, 213, 213)-net over F3, using
(130, 130+83, 2325)-Net in Base 3 — Upper bound on s
There is no (130, 213, 2326)-net in base 3, because
- 1 times m-reduction [i] would yield (130, 212, 2326)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 142564 224851 745877 263931 122425 627864 131068 818530 237423 654227 299668 096792 873718 306809 749828 991936 770909 > 3212 [i]