Best Known (55, 55+49, s)-Nets in Base 3
(55, 55+49, 56)-Net over F3 — Constructive and digital
Digital (55, 104, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 52, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(55, 55+49, 69)-Net over F3 — Digital
Digital (55, 104, 69)-net over F3, using
(55, 55+49, 523)-Net in Base 3 — Upper bound on s
There is no (55, 104, 524)-net in base 3, because
- 1 times m-reduction [i] would yield (55, 103, 524)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 13 975871 631271 865624 154684 179010 818526 398617 988673 > 3103 [i]