Best Known (119, 189, s)-Nets in Base 3
(119, 189, 156)-Net over F3 — Constructive and digital
Digital (119, 189, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (119, 194, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 97, 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, 97, 78)-net over F9, using
(119, 189, 222)-Net over F3 — Digital
Digital (119, 189, 222)-net over F3, using
(119, 189, 2588)-Net in Base 3 — Upper bound on s
There is no (119, 189, 2589)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 519023 466190 811866 723402 626787 703447 166441 502094 826771 321488 330702 167625 913979 651508 877323 > 3189 [i]