Best Known (74−42, 74, s)-Nets in Base 32
(74−42, 74, 162)-Net over F32 — Constructive and digital
Digital (32, 74, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (32, 76, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 51, 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 (3, 25, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(74−42, 74, 274)-Net over F32 — Digital
Digital (32, 74, 274)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3274, 274, F32, 2, 42) (dual of [(274, 2), 474, 43]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3272, 273, F32, 2, 42) (dual of [(273, 2), 474, 43]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,503P) [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3272, 273, F32, 2, 42) (dual of [(273, 2), 474, 43]-NRT-code), using
(74−42, 74, 288)-Net in Base 32 — Constructive
(32, 74, 288)-net in base 32, using
- t-expansion [i] based on (31, 74, 288)-net in base 32, using
- 3 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- 3 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
(74−42, 74, 321)-Net in Base 32
(32, 74, 321)-net in base 32, using
- 6 times m-reduction [i] based on (32, 80, 321)-net in base 32, using
- base change [i] based on digital (2, 50, 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, 50, 321)-net over F256, using
(74−42, 74, 56352)-Net in Base 32 — Upper bound on s
There is no (32, 74, 56353)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2405 677024 971193 540643 376266 122408 716264 192307 417446 064137 346531 176716 297369 987474 457480 004328 943061 102825 499424 > 3274 [i]