Best Known (155, 155+57, s)-Nets in Base 3
(155, 155+57, 288)-Net over F3 — Constructive and digital
Digital (155, 212, 288)-net over F3, using
- 4 times m-reduction [i] based on digital (155, 216, 288)-net over F3, using
- trace code for nets [i] based on digital (11, 72, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- trace code for nets [i] based on digital (11, 72, 96)-net over F27, using
(155, 155+57, 677)-Net over F3 — Digital
Digital (155, 212, 677)-net over F3, using
(155, 155+57, 22227)-Net in Base 3 — Upper bound on s
There is no (155, 212, 22228)-net in base 3, because
- 1 times m-reduction [i] would yield (155, 211, 22228)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 47090 929340 073816 928391 330848 115356 257765 280784 781947 758257 406611 092691 227880 730843 634521 568401 832961 > 3211 [i]