Best Known (39, 39+64, s)-Nets in Base 27
(39, 39+64, 116)-Net over F27 — Constructive and digital
Digital (39, 103, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 35, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 68, 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 (3, 35, 52)-net over F27, using
(39, 39+64, 224)-Net in Base 27 — Constructive
(39, 103, 224)-net in base 27, using
- 1 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
(39, 39+64, 271)-Net over F27 — Digital
Digital (39, 103, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(39, 39+64, 298)-Net in Base 27
(39, 103, 298)-net in base 27, using
- 5 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
(39, 39+64, 19895)-Net in Base 27 — Upper bound on s
There is no (39, 103, 19896)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2698 730395 875858 164977 406250 630587 982668 949405 483959 362351 427251 138468 787736 186750 911327 543585 164910 030976 478169 036228 064255 470287 708650 926257 539073 > 27103 [i]