Best Known (26, 26+37, s)-Nets in Base 256
(26, 26+37, 522)-Net over F256 — Constructive and digital
Digital (26, 63, 522)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (4, 41, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256 (see above)
- digital (4, 22, 261)-net over F256, using
(26, 26+37, 1026)-Net over F256 — Digital
Digital (26, 63, 1026)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25663, 1026, F256, 2, 37) (dual of [(1026, 2), 1989, 38]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25661, 1025, F256, 2, 37) (dual of [(1025, 2), 1989, 38]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,2012P) [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]
- extended algebraic-geometric NRT-code AGe(2;F,2012P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25661, 1025, F256, 2, 37) (dual of [(1025, 2), 1989, 38]-NRT-code), using
(26, 26+37, 5843028)-Net in Base 256 — Upper bound on s
There is no (26, 63, 5843029)-net in base 256, because
- 1 times m-reduction [i] would yield (26, 62, 5843029)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 204587 194232 617750 954217 262892 291420 041697 149278 943327 086294 454681 807121 045678 453593 408976 804806 851756 738803 804364 019623 237006 002527 190491 619691 644486 > 25662 [i]