Best Known (17, 33, s)-Nets in Base 32
(17, 33, 142)-Net over F32 — Constructive and digital
Digital (17, 33, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 66)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 21, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (4, 12, 66)-net over F32, using
(17, 33, 261)-Net in Base 32 — Constructive
(17, 33, 261)-net in base 32, using
- 321 times duplication [i] based on (16, 32, 261)-net in base 32, using
- base change [i] based on digital (4, 20, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 20, 261)-net over F256, using
(17, 33, 531)-Net over F32 — Digital
Digital (17, 33, 531)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3233, 531, F32, 16) (dual of [531, 498, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3233, 1032, F32, 16) (dual of [1032, 999, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3231, 1024, F32, 16) (dual of [1024, 993, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3225, 1024, F32, 13) (dual of [1024, 999, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-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(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3233, 1032, F32, 16) (dual of [1032, 999, 17]-code), using
(17, 33, 196364)-Net in Base 32 — Upper bound on s
There is no (17, 33, 196365)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 46 768363 593483 096362 319442 613856 850068 194392 844239 > 3233 [i]