Best Known (79−34, 79, s)-Nets in Base 27
(79−34, 79, 222)-Net over F27 — Constructive and digital
Digital (45, 79, 222)-net over F27, using
- 1 times m-reduction [i] based on digital (45, 80, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 15, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (6, 23, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 42, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 15, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(79−34, 79, 370)-Net in Base 27 — Constructive
(45, 79, 370)-net in base 27, using
- t-expansion [i] based on (43, 79, 370)-net in base 27, using
- 29 times m-reduction [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
- 29 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(79−34, 79, 1369)-Net over F27 — Digital
Digital (45, 79, 1369)-net over F27, using
(79−34, 79, 1237657)-Net in Base 27 — Upper bound on s
There is no (45, 79, 1237658)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 119602 740358 214767 330548 134027 934770 933138 646297 061686 809457 422905 116846 941859 673574 838166 578745 474066 279994 813445 > 2779 [i]