Best Known (77, 77+23, s)-Nets in Base 32
(77, 77+23, 95358)-Net over F32 — Constructive and digital
Digital (77, 100, 95358)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (66, 89, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- digital (0, 11, 33)-net over F32, using
(77, 77+23, 190651)-Net in Base 32 — Constructive
(77, 100, 190651)-net in base 32, using
- 322 times duplication [i] based on (75, 98, 190651)-net in base 32, using
- base change [i] based on digital (47, 70, 190651)-net over F128, using
- 1281 times duplication [i] based on digital (46, 69, 190651)-net over F128, using
- net defined by OOA [i] based on linear OOA(12869, 190651, F128, 23, 23) (dual of [(190651, 23), 4384904, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12869, 2097162, F128, 23) (dual of [2097162, 2097093, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12869, 2097163, F128, 23) (dual of [2097163, 2097094, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12869, 2097163, F128, 23) (dual of [2097163, 2097094, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12869, 2097162, F128, 23) (dual of [2097162, 2097093, 24]-code), using
- net defined by OOA [i] based on linear OOA(12869, 190651, F128, 23, 23) (dual of [(190651, 23), 4384904, 24]-NRT-code), using
- 1281 times duplication [i] based on digital (46, 69, 190651)-net over F128, using
- base change [i] based on digital (47, 70, 190651)-net over F128, using
(77, 77+23, 2028077)-Net over F32 — Digital
Digital (77, 100, 2028077)-net over F32, using
(77, 77+23, large)-Net in Base 32 — Upper bound on s
There is no (77, 100, large)-net in base 32, because
- 21 times m-reduction [i] would yield (77, 79, large)-net in base 32, but