Best Known (105, 159, s)-Nets in Base 3
(105, 159, 156)-Net over F3 — Constructive and digital
Digital (105, 159, 156)-net over F3, using
- 7 times m-reduction [i] based on digital (105, 166, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 83, 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, 83, 78)-net over F9, using
(105, 159, 248)-Net over F3 — Digital
Digital (105, 159, 248)-net over F3, using
(105, 159, 3498)-Net in Base 3 — Upper bound on s
There is no (105, 159, 3499)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7336 867700 711115 228263 437278 255380 998093 982832 869981 875882 461816 702620 004507 > 3159 [i]