Best Known (60−28, 60, s)-Nets in Base 32
(60−28, 60, 218)-Net over F32 — Constructive and digital
Digital (32, 60, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 21, 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 (11, 39, 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 (7, 21, 98)-net over F32, using
(60−28, 60, 290)-Net in Base 32 — Constructive
(32, 60, 290)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 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
- (18, 46, 257)-net in base 32, using
- 2 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- base change [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
- 2 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- digital (0, 14, 33)-net over F32, using
(60−28, 60, 874)-Net over F32 — Digital
Digital (32, 60, 874)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3260, 874, F32, 28) (dual of [874, 814, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3260, 1041, F32, 28) (dual of [1041, 981, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3255, 1024, F32, 28) (dual of [1024, 969, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3243, 1024, F32, 22) (dual of [1024, 981, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3260, 1041, F32, 28) (dual of [1041, 981, 29]-code), using
(60−28, 60, 550469)-Net in Base 32 — Upper bound on s
There is no (32, 60, 550470)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 037057 646359 769760 514471 463992 110593 486186 769569 227790 732713 589981 388830 259845 827579 351584 > 3260 [i]