Best Known (250−103, 250, s)-Nets in Base 3
(250−103, 250, 156)-Net over F3 — Constructive and digital
Digital (147, 250, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 125, 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
(250−103, 250, 209)-Net over F3 — Digital
Digital (147, 250, 209)-net over F3, using
(250−103, 250, 2069)-Net in Base 3 — Upper bound on s
There is no (147, 250, 2070)-net in base 3, because
- 1 times m-reduction [i] would yield (147, 249, 2070)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 63835 461190 686477 660825 371549 694622 853715 648613 749239 654917 392757 853202 220754 756836 418440 419018 595425 479650 899833 057217 > 3249 [i]