Best Known (27, 66, s)-Nets in Base 256
(27, 66, 522)-Net over F256 — Constructive and digital
Digital (27, 66, 522)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (4, 43, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256 (see above)
- digital (4, 23, 261)-net over F256, using
(27, 66, 1027)-Net over F256 — Digital
Digital (27, 66, 1027)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25666, 1027, F256, 2, 39) (dual of [(1027, 2), 1988, 40]-NRT-code), using
- construction X applied to AG(2;F,2008P) ⊂ AG(2;F,2012P) [i] based on
- linear OOA(25663, 1024, F256, 2, 39) (dual of [(1024, 2), 1985, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,2008P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- linear OOA(25659, 1024, F256, 2, 35) (dual of [(1024, 2), 1989, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,2012P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025 (see above)
- linear OOA(2563, 3, F256, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2563, 256, F256, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;509,256) [i]
- discarding factors / shortening the dual code based on linear OOA(2563, 256, F256, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
- linear OOA(25663, 1024, F256, 2, 39) (dual of [(1024, 2), 1985, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,2008P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- construction X applied to AG(2;F,2008P) ⊂ AG(2;F,2012P) [i] based on
(27, 66, 5387536)-Net in Base 256 — Upper bound on s
There is no (27, 66, 5387537)-net in base 256, because
- 1 times m-reduction [i] would yield (27, 65, 5387537)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 3 432398 910977 995301 586719 095926 877623 941355 809654 210158 185090 447063 399513 505156 677271 403592 509098 466828 293694 366853 852580 309328 145230 314712 350011 930592 297216 > 25665 [i]