Best Known (53, 105, s)-Nets in Base 27
(53, 105, 196)-Net over F27 — Constructive and digital
Digital (53, 105, 196)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 35, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (18, 70, 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 (9, 35, 88)-net over F27, using
(53, 105, 370)-Net in Base 27 — Constructive
(53, 105, 370)-net in base 27, using
- t-expansion [i] based on (43, 105, 370)-net in base 27, using
- 3 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
- 3 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(53, 105, 689)-Net over F27 — Digital
Digital (53, 105, 689)-net over F27, using
(53, 105, 244795)-Net in Base 27 — Upper bound on s
There is no (53, 105, 244796)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 964368 457711 083499 687162 203877 822976 853480 751920 231980 109934 179307 757996 472975 698913 715136 671057 128587 189947 693201 412351 789461 569047 925011 556303 830921 > 27105 [i]