Best Known (27, 51, s)-Nets in Base 32
(27, 51, 196)-Net over F32 — Constructive and digital
Digital (27, 51, 196)-net over F32, using
- 2 times m-reduction [i] based on digital (27, 53, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 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, 33, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 20, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(27, 51, 290)-Net in Base 32 — Constructive
(27, 51, 290)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- (15, 39, 257)-net in base 32, using
- 1 times m-reduction [i] based on (15, 40, 257)-net in base 32, using
- base change [i] based on digital (0, 25, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 25, 257)-net over F256, using
- 1 times m-reduction [i] based on (15, 40, 257)-net in base 32, using
- digital (0, 12, 33)-net over F32, using
(27, 51, 760)-Net over F32 — Digital
Digital (27, 51, 760)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3251, 760, F32, 24) (dual of [760, 709, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3251, 1038, F32, 24) (dual of [1038, 987, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- linear OA(3247, 1024, F32, 24) (dual of [1024, 977, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3237, 1024, F32, 19) (dual of [1024, 987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(324, 14, F32, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3251, 1038, F32, 24) (dual of [1038, 987, 25]-code), using
(27, 51, 425481)-Net in Base 32 — Upper bound on s
There is no (27, 51, 425482)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 57896 161825 025783 566625 456999 569538 819363 583537 617640 510267 130786 630590 474624 > 3251 [i]