Best Known (220−61, 220, s)-Nets in Base 3
(220−61, 220, 288)-Net over F3 — Constructive and digital
Digital (159, 220, 288)-net over F3, using
- 2 times m-reduction [i] based on digital (159, 222, 288)-net over F3, using
- trace code for nets [i] based on digital (11, 74, 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, 74, 96)-net over F27, using
(220−61, 220, 626)-Net over F3 — Digital
Digital (159, 220, 626)-net over F3, using
(220−61, 220, 18282)-Net in Base 3 — Upper bound on s
There is no (159, 220, 18283)-net in base 3, because
- 1 times m-reduction [i] would yield (159, 219, 18283)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 308 784013 754377 688677 128171 451885 462806 798411 590972 828763 196936 603972 593866 773640 623879 538391 907685 162045 > 3219 [i]