Best Known (66, 66+18, s)-Nets in Base 32
(66, 66+18, 116596)-Net over F32 — Constructive and digital
Digital (66, 84, 116596)-net over F32, using
- (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 (51, 69, 116508)-net over F32, using
- net defined by OOA [i] based on linear OOA(3269, 116508, F32, 18, 18) (dual of [(116508, 18), 2097075, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3269, 1048572, F32, 18) (dual of [1048572, 1048503, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3269, 1048572, F32, 18) (dual of [1048572, 1048503, 19]-code), using
- net defined by OOA [i] based on linear OOA(3269, 116508, F32, 18, 18) (dual of [(116508, 18), 2097075, 19]-NRT-code), using
- digital (6, 15, 88)-net over F32, using
(66, 66+18, 932067)-Net in Base 32 — Constructive
(66, 84, 932067)-net in base 32, using
- base change [i] based on digital (52, 70, 932067)-net over F64, using
- 641 times duplication [i] based on digital (51, 69, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- 641 times duplication [i] based on digital (51, 69, 932067)-net over F64, using
(66, 66+18, 6335717)-Net over F32 — Digital
Digital (66, 84, 6335717)-net over F32, using
(66, 66+18, 6642764)-Net in Base 32
(66, 84, 6642764)-net in base 32, using
- base change [i] based on digital (52, 70, 6642764)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6470, 6642764, F64, 18) (dual of [6642764, 6642694, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, large, F64, 18) (dual of [large, large−70, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times code embedding in larger space [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, large, F64, 18) (dual of [large, large−70, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6470, 6642764, F64, 18) (dual of [6642764, 6642694, 19]-code), using
(66, 66+18, large)-Net in Base 32 — Upper bound on s
There is no (66, 84, large)-net in base 32, because
- 16 times m-reduction [i] would yield (66, 68, large)-net in base 32, but