Best Known (93, 109, s)-Nets in Base 32
(93, 109, 1310753)-Net over F32 — Constructive and digital
Digital (93, 109, 1310753)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (25, 33, 262178)-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 (21, 29, 262145)-net over F32, using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (60, 76, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (25, 33, 262178)-net over F32, using
(93, 109, 2097150)-Net in Base 32 — Constructive
(93, 109, 2097150)-net in base 32, using
- 321 times duplication [i] based on (92, 108, 2097150)-net in base 32, using
- base change [i] based on digital (74, 90, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6490, 2097150, F64, 18, 16) (dual of [(2097150, 18), 37748610, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(6490, 8388601, F64, 2, 16) (dual of [(8388601, 2), 16777112, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6490, 8388602, F64, 2, 16) (dual of [(8388602, 2), 16777114, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6490, 8388602, F64, 2, 16) (dual of [(8388602, 2), 16777114, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(6490, 8388601, F64, 2, 16) (dual of [(8388601, 2), 16777112, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6490, 2097150, F64, 18, 16) (dual of [(2097150, 18), 37748610, 17]-NRT-code), using
- base change [i] based on digital (74, 90, 2097150)-net over F64, using
(93, 109, large)-Net over F32 — Digital
Digital (93, 109, large)-net over F32, using
- t-expansion [i] based on digital (87, 109, large)-net over F32, using
- 1 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(93, 109, large)-Net in Base 32 — Upper bound on s
There is no (93, 109, large)-net in base 32, because
- 14 times m-reduction [i] would yield (93, 95, large)-net in base 32, but