Best Known (44−26, 44, s)-Nets in Base 27
(44−26, 44, 108)-Net over F27 — Constructive and digital
Digital (18, 44, 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
(44−26, 44, 148)-Net over F27 — Digital
Digital (18, 44, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
(44−26, 44, 172)-Net in Base 27 — Constructive
(18, 44, 172)-net in base 27, using
- base change [i] based on digital (7, 33, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(44−26, 44, 190)-Net in Base 27
(18, 44, 190)-net in base 27, using
- 4 times m-reduction [i] based on (18, 48, 190)-net in base 27, using
- base change [i] based on digital (6, 36, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 36, 190)-net over F81, using
(44−26, 44, 15235)-Net in Base 27 — Upper bound on s
There is no (18, 44, 15236)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 955 220445 405112 855441 055141 215370 190043 015936 559852 299554 744009 > 2744 [i]