Best Known (61, 61+18, s)-Nets in Base 32
(61, 61+18, 116552)-Net over F32 — Constructive and digital
Digital (61, 79, 116552)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (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 (1, 10, 44)-net over F32, using
(61, 61+18, 233019)-Net in Base 32 — Constructive
(61, 79, 233019)-net in base 32, using
- net defined by OOA [i] based on OOA(3279, 233019, S32, 18, 18), using
- OA 9-folding and stacking [i] based on OA(3279, 2097171, S32, 18), using
- discarding parts of the base [i] based on linear OA(12856, 2097171, F128, 18) (dual of [2097171, 2097115, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(12856, 2097171, F128, 18) (dual of [2097171, 2097115, 19]-code), using
- OA 9-folding and stacking [i] based on OA(3279, 2097171, S32, 18), using
(61, 61+18, 2286155)-Net over F32 — Digital
Digital (61, 79, 2286155)-net over F32, using
(61, 61+18, large)-Net in Base 32 — Upper bound on s
There is no (61, 79, large)-net in base 32, because
- 16 times m-reduction [i] would yield (61, 63, large)-net in base 32, but