Best Known (181−66, 181, s)-Nets in Base 3
(181−66, 181, 156)-Net over F3 — Constructive and digital
Digital (115, 181, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (115, 186, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 93, 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, 93, 78)-net over F9, using
(181−66, 181, 223)-Net over F3 — Digital
Digital (115, 181, 223)-net over F3, using
(181−66, 181, 2692)-Net in Base 3 — Upper bound on s
There is no (115, 181, 2693)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 231 303655 198112 062131 241085 461019 728765 089251 413751 635368 290500 792188 796459 817858 637963 > 3181 [i]