Best Known (98−54, 98, s)-Nets in Base 27
(98−54, 98, 176)-Net over F27 — Constructive and digital
Digital (44, 98, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 34, 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 (10, 64, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (7, 34, 82)-net over F27, using
(98−54, 98, 343)-Net over F27 — Digital
Digital (44, 98, 343)-net over F27, using
(98−54, 98, 370)-Net in Base 27 — Constructive
(44, 98, 370)-net in base 27, using
- t-expansion [i] based on (43, 98, 370)-net in base 27, using
- 10 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
- 10 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(98−54, 98, 65865)-Net in Base 27 — Upper bound on s
There is no (44, 98, 65866)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 187 780838 337369 910047 596804 798458 672994 997237 688898 879220 392054 133918 628314 845544 454202 586988 942411 550204 045984 107033 929372 420914 194978 653489 > 2798 [i]