Best Known (97, 97+44, s)-Nets in Base 3
(97, 97+44, 156)-Net over F3 — Constructive and digital
Digital (97, 141, 156)-net over F3, using
- 9 times m-reduction [i] based on digital (97, 150, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 75, 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, 75, 78)-net over F9, using
(97, 97+44, 291)-Net over F3 — Digital
Digital (97, 141, 291)-net over F3, using
(97, 97+44, 5151)-Net in Base 3 — Upper bound on s
There is no (97, 141, 5152)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18 840065 807025 870591 929208 962378 844039 346979 637209 532405 060801 149121 > 3141 [i]