Best Known (55, 108, s)-Nets in Base 27
(55, 108, 204)-Net over F27 — Constructive and digital
Digital (55, 108, 204)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 37, 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
- digital (18, 71, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- digital (11, 37, 96)-net over F27, using
(55, 108, 370)-Net in Base 27 — Constructive
(55, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
(55, 108, 746)-Net over F27 — Digital
Digital (55, 108, 746)-net over F27, using
(55, 108, 315437)-Net in Base 27 — Upper bound on s
There is no (55, 108, 315438)-net in base 27, because
- 1 times m-reduction [i] would yield (55, 107, 315438)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1431 975323 377570 458064 850384 120892 863593 110932 825866 412987 961321 022223 899808 020199 125574 797239 091881 426934 288351 738450 568833 250665 033354 228996 179348 311181 > 27107 [i]