Best Known (244−72, 244, s)-Nets in Base 3
(244−72, 244, 264)-Net over F3 — Constructive and digital
Digital (172, 244, 264)-net over F3, using
- 31 times duplication [i] based on digital (171, 243, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 81, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- trace code for nets [i] based on digital (9, 81, 88)-net over F27, using
(244−72, 244, 556)-Net over F3 — Digital
Digital (172, 244, 556)-net over F3, using
(244−72, 244, 12197)-Net in Base 3 — Upper bound on s
There is no (172, 244, 12198)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 262 008834 087899 813352 262282 449403 460831 553735 399578 161306 165338 458060 482102 160467 735373 645057 507159 932318 910248 516169 > 3244 [i]