Best Known (32, 42, s)-Nets in Base 32
(32, 42, 209749)-Net over F32 — Constructive and digital
Digital (32, 42, 209749)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (27, 37, 209716)-net over F32, using
- net defined by OOA [i] based on linear OOA(3237, 209716, F32, 10, 10) (dual of [(209716, 10), 2097123, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3237, 1048580, F32, 10) (dual of [1048580, 1048543, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(3237, 1048576, F32, 10) (dual of [1048576, 1048539, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3233, 1048576, F32, 9) (dual of [1048576, 1048543, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- OA 5-folding and stacking [i] based on linear OA(3237, 1048580, F32, 10) (dual of [1048580, 1048543, 11]-code), using
- net defined by OOA [i] based on linear OOA(3237, 209716, F32, 10, 10) (dual of [(209716, 10), 2097123, 11]-NRT-code), using
- digital (0, 5, 33)-net over F32, using
(32, 42, 419432)-Net in Base 32 — Constructive
(32, 42, 419432)-net in base 32, using
- base change [i] based on digital (20, 30, 419432)-net over F128, using
- net defined by OOA [i] based on linear OOA(12830, 419432, F128, 10, 10) (dual of [(419432, 10), 4194290, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(12830, 2097160, F128, 10) (dual of [2097160, 2097130, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(12830, 2097160, F128, 10) (dual of [2097160, 2097130, 11]-code), using
- net defined by OOA [i] based on linear OOA(12830, 419432, F128, 10, 10) (dual of [(419432, 10), 4194290, 11]-NRT-code), using
(32, 42, 1413918)-Net over F32 — Digital
Digital (32, 42, 1413918)-net over F32, using
(32, 42, large)-Net in Base 32 — Upper bound on s
There is no (32, 42, large)-net in base 32, because
- 8 times m-reduction [i] would yield (32, 34, large)-net in base 32, but