Best Known (130, 130+70, s)-Nets in Base 3
(130, 130+70, 156)-Net over F3 — Constructive and digital
Digital (130, 200, 156)-net over F3, using
- 16 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+70, 274)-Net over F3 — Digital
Digital (130, 200, 274)-net over F3, using
(130, 130+70, 3669)-Net in Base 3 — Upper bound on s
There is no (130, 200, 3670)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 267180 821817 926420 888453 881191 483703 684142 626377 068775 201034 965073 397729 464022 983285 269406 262625 > 3200 [i]