Best Known (29, 29+39, s)-Nets in Base 256
(29, 29+39, 524)-Net over F256 — Constructive and digital
Digital (29, 68, 524)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- digital (5, 44, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256 (see above)
- digital (5, 24, 262)-net over F256, using
(29, 29+39, 1222)-Net over F256 — Digital
Digital (29, 68, 1222)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25668, 1222, F256, 39) (dual of [1222, 1154, 40]-code), using
- 192 step Varšamov–Edel lengthening with (ri) = (3, 8 times 0, 1, 47 times 0, 1, 134 times 0) [i] based on linear OA(25663, 1025, F256, 39) (dual of [1025, 962, 40]-code), using
- extended algebraic-geometric code AGe(F,985P) [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 code AGe(F,985P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- 192 step Varšamov–Edel lengthening with (ri) = (3, 8 times 0, 1, 47 times 0, 1, 134 times 0) [i] based on linear OA(25663, 1025, F256, 39) (dual of [1025, 962, 40]-code), using
(29, 29+39, large)-Net in Base 256 — Upper bound on s
There is no (29, 68, large)-net in base 256, because
- 37 times m-reduction [i] would yield (29, 31, large)-net in base 256, but