Best Known (22, 42, s)-Nets in Base 32
(22, 42, 174)-Net over F32 — Constructive and digital
Digital (22, 42, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 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 (7, 27, 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 (5, 15, 76)-net over F32, using
(22, 42, 290)-Net in Base 32 — Constructive
(22, 42, 290)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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
- (12, 32, 257)-net in base 32, using
- base change [i] based on digital (0, 20, 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, 20, 257)-net over F256, using
- digital (0, 10, 33)-net over F32, using
(22, 42, 645)-Net over F32 — Digital
Digital (22, 42, 645)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3242, 645, F32, 20) (dual of [645, 603, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3242, 1035, F32, 20) (dual of [1035, 993, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3239, 1024, F32, 20) (dual of [1024, 985, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3242, 1035, F32, 20) (dual of [1035, 993, 21]-code), using
(22, 42, 306363)-Net in Base 32 — Upper bound on s
There is no (22, 42, 306364)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1645 506417 573383 365295 212514 090257 097861 951469 722267 610972 871073 > 3242 [i]