Best Known (132, 247, s)-Nets in Base 3
(132, 247, 85)-Net over F3 — Constructive and digital
Digital (132, 247, 85)-net over F3, using
- t-expansion [i] based on digital (131, 247, 85)-net over F3, using
- 2 times m-reduction [i] based on digital (131, 249, 85)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (27, 86, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- digital (45, 163, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- digital (27, 86, 37)-net over F3, using
- (u, u+v)-construction [i] based on
- 2 times m-reduction [i] based on digital (131, 249, 85)-net over F3, using
(132, 247, 147)-Net over F3 — Digital
Digital (132, 247, 147)-net over F3, using
(132, 247, 1209)-Net in Base 3 — Upper bound on s
There is no (132, 247, 1210)-net in base 3, because
- 1 times m-reduction [i] would yield (132, 246, 1210)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2395 458095 519126 016607 174522 288867 543518 118585 450828 487267 675179 432708 393369 659624 823793 327248 556605 500306 286084 267205 > 3246 [i]