Best Known (79, 79+29, s)-Nets in Base 32
(79, 79+29, 2444)-Net over F32 — Constructive and digital
Digital (79, 108, 2444)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (56, 85, 2340)-net over F32, using
- net defined by OOA [i] based on linear OOA(3285, 2340, F32, 29, 29) (dual of [(2340, 29), 67775, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3285, 32761, F32, 29) (dual of [32761, 32676, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 32768, F32, 29) (dual of [32768, 32683, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(3285, 32768, F32, 29) (dual of [32768, 32683, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3285, 32761, F32, 29) (dual of [32761, 32676, 30]-code), using
- net defined by OOA [i] based on linear OOA(3285, 2340, F32, 29, 29) (dual of [(2340, 29), 67775, 30]-NRT-code), using
- digital (9, 23, 104)-net over F32, using
(79, 79+29, 18726)-Net in Base 32 — Constructive
(79, 108, 18726)-net in base 32, using
- base change [i] based on digital (61, 90, 18726)-net over F64, using
- net defined by OOA [i] based on linear OOA(6490, 18726, F64, 29, 29) (dual of [(18726, 29), 542964, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6490, 262165, F64, 29) (dual of [262165, 262075, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(6490, 262168, F64, 29) (dual of [262168, 262078, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,11]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6467, 262145, F64, 23) (dual of [262145, 262078, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to C([0,14]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6490, 262168, F64, 29) (dual of [262168, 262078, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6490, 262165, F64, 29) (dual of [262165, 262075, 30]-code), using
- net defined by OOA [i] based on linear OOA(6490, 18726, F64, 29, 29) (dual of [(18726, 29), 542964, 30]-NRT-code), using
(79, 79+29, 232942)-Net over F32 — Digital
Digital (79, 108, 232942)-net over F32, using
(79, 79+29, large)-Net in Base 32 — Upper bound on s
There is no (79, 108, large)-net in base 32, because
- 27 times m-reduction [i] would yield (79, 81, large)-net in base 32, but