Best Known (107, 107+48, s)-Nets in Base 3
(107, 107+48, 156)-Net over F3 — Constructive and digital
Digital (107, 155, 156)-net over F3, using
- 15 times m-reduction [i] based on digital (107, 170, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 85, 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, 85, 78)-net over F9, using
(107, 107+48, 322)-Net over F3 — Digital
Digital (107, 155, 322)-net over F3, using
(107, 107+48, 5888)-Net in Base 3 — Upper bound on s
There is no (107, 155, 5889)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 90 043673 463715 718533 787520 896097 896332 436551 700074 981658 979230 447575 775457 > 3155 [i]