Best Known (71, 91, s)-Nets in Base 32
(71, 91, 104922)-Net over F32 — Constructive and digital
Digital (71, 91, 104922)-net over F32, using
- 321 times duplication [i] based on digital (70, 90, 104922)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (57, 77, 104858)-net over F32, using
- net defined by OOA [i] based on linear OOA(3277, 104858, F32, 20, 20) (dual of [(104858, 20), 2097083, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3277, 1048580, F32, 20) (dual of [1048580, 1048503, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- OA 10-folding and stacking [i] based on linear OA(3277, 1048580, F32, 20) (dual of [1048580, 1048503, 21]-code), using
- net defined by OOA [i] based on linear OOA(3277, 104858, F32, 20, 20) (dual of [(104858, 20), 2097083, 21]-NRT-code), using
- digital (3, 13, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(71, 91, 209718)-Net in Base 32 — Constructive
(71, 91, 209718)-net in base 32, using
- base change [i] based on digital (45, 65, 209718)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 209718, F128, 20, 20) (dual of [(209718, 20), 4194295, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(12865, 2097180, F128, 20) (dual of [2097180, 2097115, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12865, 2097183, F128, 20) (dual of [2097183, 2097118, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(11) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(19) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12865, 2097183, F128, 20) (dual of [2097183, 2097118, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(12865, 2097180, F128, 20) (dual of [2097180, 2097115, 21]-code), using
- net defined by OOA [i] based on linear OOA(12865, 209718, F128, 20, 20) (dual of [(209718, 20), 4194295, 21]-NRT-code), using
(71, 91, 4137433)-Net over F32 — Digital
Digital (71, 91, 4137433)-net over F32, using
(71, 91, large)-Net in Base 32 — Upper bound on s
There is no (71, 91, large)-net in base 32, because
- 18 times m-reduction [i] would yield (71, 73, large)-net in base 32, but