Best Known (247−142, 247, s)-Nets in Base 3
(247−142, 247, 72)-Net over F3 — Constructive and digital
Digital (105, 247, 72)-net over F3, using
- net from sequence [i] based on digital (105, 71)-sequence over F3, using
- base reduction for sequences [i] based on digital (17, 71)-sequence over F9, using
- s-reduction based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- s-reduction based on digital (17, 73)-sequence over F9, using
- base reduction for sequences [i] based on digital (17, 71)-sequence over F9, using
(247−142, 247, 104)-Net over F3 — Digital
Digital (105, 247, 104)-net over F3, using
- t-expansion [i] based on digital (102, 247, 104)-net over F3, using
- net from sequence [i] based on digital (102, 103)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 102 and N(F) ≥ 104, using
- net from sequence [i] based on digital (102, 103)-sequence over F3, using
(247−142, 247, 555)-Net in Base 3 — Upper bound on s
There is no (105, 247, 556)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7421 951929 558862 166356 264642 597482 498488 667894 047848 801272 799143 602044 411406 606925 030077 540739 527909 197264 356088 574417 > 3247 [i]