Best Known (45, 45+62, s)-Nets in Base 27
(45, 45+62, 164)-Net over F27 — Constructive and digital
Digital (45, 107, 164)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 38, 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 (7, 69, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 38, 82)-net over F27, using
(45, 45+62, 281)-Net over F27 — Digital
Digital (45, 107, 281)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(27107, 281, F27, 2, 62) (dual of [(281, 2), 455, 63]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(27107, 282, F27, 2, 62) (dual of [(282, 2), 457, 63]-NRT-code), using
- construction X applied to AG(2;F,495P) ⊂ AG(2;F,499P) [i] based on
- linear OOA(27104, 279, F27, 2, 62) (dual of [(279, 2), 454, 63]-NRT-code), using algebraic-geometric NRT-code AG(2;F,495P) [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280, using
- linear OOA(27100, 279, F27, 2, 58) (dual of [(279, 2), 458, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,499P) [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280 (see above)
- linear OOA(273, 3, F27, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(273, 27, F27, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;51,27) [i]
- discarding factors / shortening the dual code based on linear OOA(273, 27, F27, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
- construction X applied to AG(2;F,495P) ⊂ AG(2;F,499P) [i] based on
- discarding factors / shortening the dual code based on linear OOA(27107, 282, F27, 2, 62) (dual of [(282, 2), 457, 63]-NRT-code), using
(45, 45+62, 370)-Net in Base 27 — Constructive
(45, 107, 370)-net in base 27, using
- t-expansion [i] based on (43, 107, 370)-net in base 27, using
- 1 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
- 1 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(45, 45+62, 41629)-Net in Base 27 — Upper bound on s
There is no (45, 107, 41630)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1432 141303 983423 726876 281653 429580 838361 422225 929364 084500 367956 283804 363579 681406 649023 609506 039179 724994 537808 827828 103188 568584 982083 399855 124870 006809 > 27107 [i]