Best Known (32, 32+44, s)-Nets in Base 27
(32, 32+44, 140)-Net over F27 — Constructive and digital
Digital (32, 76, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 26, 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 (6, 50, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 26, 64)-net over F27, using
(32, 32+44, 215)-Net over F27 — Digital
Digital (32, 76, 215)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2776, 215, F27, 2, 44) (dual of [(215, 2), 354, 45]-NRT-code), using
- construction X applied to AG(2;F,369P) ⊂ AG(2;F,378P) [i] based on
- linear OOA(2768, 207, F27, 2, 44) (dual of [(207, 2), 346, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,369P) [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- linear OOA(2759, 207, F27, 2, 35) (dual of [(207, 2), 355, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,378P) [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208 (see above)
- linear OOA(278, 8, F27, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(278, 27, F27, 2, 8) (dual of [(27, 2), 46, 9]-NRT-code), using
- Reed–Solomon NRT-code RS(2;46,27) [i]
- discarding factors / shortening the dual code based on linear OOA(278, 27, F27, 2, 8) (dual of [(27, 2), 46, 9]-NRT-code), using
- construction X applied to AG(2;F,369P) ⊂ AG(2;F,378P) [i] based on
(32, 32+44, 224)-Net in Base 27 — Constructive
(32, 76, 224)-net in base 27, using
- base change [i] based on digital (13, 57, 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
(32, 32+44, 298)-Net in Base 27
(32, 76, 298)-net in base 27, using
- 4 times m-reduction [i] based on (32, 80, 298)-net in base 27, using
- base change [i] based on digital (12, 60, 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, 60, 298)-net over F81, using
(32, 32+44, 30649)-Net in Base 27 — Upper bound on s
There is no (32, 76, 30650)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 6 076500 871090 596389 230768 118826 913262 282637 360632 707876 387141 742842 967938 534061 369964 040330 923242 066117 155821 > 2776 [i]