Best Known (61−35, 61, s)-Nets in Base 32
(61−35, 61, 142)-Net over F32 — Constructive and digital
Digital (26, 61, 142)-net over F32, using
- 1 times m-reduction [i] based on digital (26, 62, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (7, 43, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (1, 19, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(61−35, 61, 226)-Net over F32 — Digital
Digital (26, 61, 226)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3261, 226, F32, 2, 35) (dual of [(226, 2), 391, 36]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3259, 225, F32, 2, 35) (dual of [(225, 2), 391, 36]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,414P) [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3259, 225, F32, 2, 35) (dual of [(225, 2), 391, 36]-NRT-code), using
(61−35, 61, 259)-Net in Base 32 — Constructive
(26, 61, 259)-net in base 32, using
- 3 times m-reduction [i] based on (26, 64, 259)-net in base 32, using
- base change [i] based on digital (2, 40, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 40, 259)-net over F256, using
(61−35, 61, 321)-Net in Base 32
(26, 61, 321)-net in base 32, using
- 3 times m-reduction [i] based on (26, 64, 321)-net in base 32, using
- base change [i] based on digital (2, 40, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 40, 321)-net over F256, using
(61−35, 61, 47511)-Net in Base 32 — Upper bound on s
There is no (26, 61, 47512)-net in base 32, because
- 1 times m-reduction [i] would yield (26, 60, 47512)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 037345 901205 794730 339088 525194 691361 016200 018319 313844 665058 920499 999430 396222 998432 297429 > 3260 [i]