Best Known (54, 106, s)-Nets in Base 32
(54, 106, 240)-Net over F32 — Constructive and digital
Digital (54, 106, 240)-net over F32, using
- t-expansion [i] based on digital (51, 106, 240)-net over F32, using
- 3 times m-reduction [i] based on digital (51, 109, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 40, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 69, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 40, 120)-net over F32, using
- (u, u+v)-construction [i] based on
- 3 times m-reduction [i] based on digital (51, 109, 240)-net over F32, using
(54, 106, 513)-Net in Base 32 — Constructive
(54, 106, 513)-net in base 32, using
- t-expansion [i] based on (46, 106, 513)-net in base 32, using
- 2 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 2 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(54, 106, 887)-Net over F32 — Digital
Digital (54, 106, 887)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32106, 887, F32, 52) (dual of [887, 781, 53]-code), using
- discarding factors / shortening the dual code based on linear OA(32106, 1044, F32, 52) (dual of [1044, 938, 53]-code), using
- construction X applied to Ce(51) ⊂ Ce(44) [i] based on
- linear OA(32100, 1024, F32, 52) (dual of [1024, 924, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3286, 1024, F32, 45) (dual of [1024, 938, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(326, 20, F32, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(51) ⊂ Ce(44) [i] based on
- discarding factors / shortening the dual code based on linear OA(32106, 1044, F32, 52) (dual of [1044, 938, 53]-code), using
(54, 106, 465907)-Net in Base 32 — Upper bound on s
There is no (54, 106, 465908)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3514 897302 393823 614747 079135 004435 860986 870068 984370 520402 219024 876561 764169 269595 660723 981756 447300 012245 815123 792439 382184 550646 792832 622020 937772 959453 924172 > 32106 [i]