Best Known (141, 141+97, s)-Nets in Base 3
(141, 141+97, 156)-Net over F3 — Constructive and digital
Digital (141, 238, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 119, 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
(141, 141+97, 206)-Net over F3 — Digital
Digital (141, 238, 206)-net over F3, using
(141, 141+97, 2078)-Net in Base 3 — Upper bound on s
There is no (141, 238, 2079)-net in base 3, because
- 1 times m-reduction [i] would yield (141, 237, 2079)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 119999 912655 490733 135556 032006 041760 294500 285678 600520 842254 077074 650128 798932 629214 002923 395970 390657 026959 999905 > 3237 [i]