Best Known (182−59, 182, s)-Nets in Base 3
(182−59, 182, 162)-Net over F3 — Constructive and digital
Digital (123, 182, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 91, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(182−59, 182, 321)-Net over F3 — Digital
Digital (123, 182, 321)-net over F3, using
(182−59, 182, 5517)-Net in Base 3 — Upper bound on s
There is no (123, 182, 5518)-net in base 3, because
- 1 times m-reduction [i] would yield (123, 181, 5518)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 228 951749 563502 603064 979468 168852 682763 407889 329550 341529 438186 802647 894959 064529 451397 > 3181 [i]