Best Known (62−39, 62, s)-Nets in Base 256
(62−39, 62, 518)-Net over F256 — Constructive and digital
Digital (23, 62, 518)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 21, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (2, 41, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256 (see above)
- digital (2, 21, 259)-net over F256, using
(62−39, 62, 642)-Net over F256 — Digital
Digital (23, 62, 642)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25662, 642, F256, 4, 39) (dual of [(642, 4), 2506, 40]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25621, 321, F256, 4, 19) (dual of [(321, 4), 1263, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,1264P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- linear OOA(25641, 321, F256, 4, 39) (dual of [(321, 4), 1243, 40]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,1244P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321 (see above)
- linear OOA(25621, 321, F256, 4, 19) (dual of [(321, 4), 1263, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
(62−39, 62, 1676450)-Net in Base 256 — Upper bound on s
There is no (23, 62, 1676451)-net in base 256, because
- 1 times m-reduction [i] would yield (23, 61, 1676451)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 799 171324 234751 914410 300610 271479 885819 037990 660657 410339 252427 965147 152890 425175 922537 985505 385865 248981 827613 135863 651407 908673 285494 173852 550496 > 25661 [i]