Best Known (32, 66, s)-Nets in Base 32
(32, 66, 196)-Net over F32 — Constructive and digital
Digital (32, 66, 196)-net over F32, using
- 2 times m-reduction [i] based on digital (32, 68, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 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 (7, 43, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 25, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(32, 66, 288)-Net in Base 32 — Constructive
(32, 66, 288)-net in base 32, using
- t-expansion [i] based on (31, 66, 288)-net in base 32, using
- 11 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
- 11 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
(32, 66, 498)-Net over F32 — Digital
Digital (32, 66, 498)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3266, 498, F32, 2, 34) (dual of [(498, 2), 930, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3266, 514, F32, 2, 34) (dual of [(514, 2), 962, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3266, 1028, F32, 34) (dual of [1028, 962, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, 1029, F32, 34) (dual of [1029, 963, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(3264, 1024, F32, 34) (dual of [1024, 960, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3261, 1024, F32, 31) (dual of [1024, 963, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(322, 5, F32, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(3266, 1029, F32, 34) (dual of [1029, 963, 35]-code), using
- OOA 2-folding [i] based on linear OA(3266, 1028, F32, 34) (dual of [1028, 962, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3266, 514, F32, 2, 34) (dual of [(514, 2), 962, 35]-NRT-code), using
(32, 66, 161467)-Net in Base 32 — Upper bound on s
There is no (32, 66, 161468)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2187 464710 558848 145134 443641 030402 086836 235095 599612 954594 283191 834474 520604 410696 800270 495957 149949 > 3266 [i]