Best Known (100−62, 100, s)-Nets in Base 27
(100−62, 100, 116)-Net over F27 — Constructive and digital
Digital (38, 100, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 34, 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, 66, 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, 34, 52)-net over F27, using
(100−62, 100, 224)-Net in Base 27 — Constructive
(38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 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
(100−62, 100, 244)-Net over F27 — Digital
Digital (38, 100, 244)-net over F27, using
- t-expansion [i] based on digital (36, 100, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(100−62, 100, 298)-Net in Base 27
(38, 100, 298)-net in base 27, using
- 4 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 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, 78, 298)-net over F81, using
(100−62, 100, 19769)-Net in Base 27 — Upper bound on s
There is no (38, 100, 19770)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 136892 294858 169172 034669 944101 931385 726234 889560 230275 543842 525582 387503 592207 575022 722010 508368 664820 253788 132255 683958 498376 300520 552806 236425 > 27100 [i]