Best Known (67, 67+38, s)-Nets in Base 32
(67, 67+38, 382)-Net over F32 — Constructive and digital
Digital (67, 105, 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, 26, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 45, 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
(67, 67+38, 862)-Net in Base 32 — Constructive
(67, 105, 862)-net in base 32, using
- base change [i] based on digital (37, 75, 862)-net over F128, using
- net defined by OOA [i] based on linear OOA(12875, 862, F128, 38, 38) (dual of [(862, 38), 32681, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(12875, 16378, F128, 38) (dual of [16378, 16303, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(12875, 16378, F128, 38) (dual of [16378, 16303, 39]-code), using
- net defined by OOA [i] based on linear OOA(12875, 862, F128, 38, 38) (dual of [(862, 38), 32681, 39]-NRT-code), using
(67, 67+38, 8848)-Net over F32 — Digital
Digital (67, 105, 8848)-net over F32, using
(67, 67+38, large)-Net in Base 32 — Upper bound on s
There is no (67, 105, large)-net in base 32, because
- 36 times m-reduction [i] would yield (67, 69, large)-net in base 32, but