Best Known (102−36, 102, s)-Nets in Base 32
(102−36, 102, 382)-Net over F32 — Constructive and digital
Digital (66, 102, 382)-net over F32, using
- 1 times m-reduction [i] based on digital (66, 103, 382)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 15, 88)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (1, 10, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32 (see above)
- digital (1, 5, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 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 (7, 25, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 44, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (6, 15, 88)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(102−36, 102, 910)-Net in Base 32 — Constructive
(66, 102, 910)-net in base 32, using
- base change [i] based on (49, 85, 910)-net in base 64, using
- 1 times m-reduction [i] based on (49, 86, 910)-net in base 64, using
- net defined by OOA [i] based on OOA(6486, 910, S64, 37, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(6486, 16381, S64, 37), using
- discarding factors based on OA(6486, 16386, S64, 37), using
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- discarding factors based on OA(6486, 16386, S64, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(6486, 16381, S64, 37), using
- net defined by OOA [i] based on OOA(6486, 910, S64, 37, 37), using
- 1 times m-reduction [i] based on (49, 86, 910)-net in base 64, using
(102−36, 102, 10940)-Net over F32 — Digital
Digital (66, 102, 10940)-net over F32, using
(102−36, 102, large)-Net in Base 32 — Upper bound on s
There is no (66, 102, large)-net in base 32, because
- 34 times m-reduction [i] would yield (66, 68, large)-net in base 32, but