Best Known (62−29, 62, s)-Nets in Base 32
(62−29, 62, 218)-Net over F32 — Constructive and digital
Digital (33, 62, 218)-net over F32, using
- 1 times m-reduction [i] based on digital (33, 63, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 22, 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 (11, 41, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (7, 22, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(62−29, 62, 301)-Net in Base 32 — Constructive
(33, 62, 301)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 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
- (18, 47, 257)-net in base 32, using
- 1 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- 1 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- digital (1, 15, 44)-net over F32, using
(62−29, 62, 874)-Net over F32 — Digital
Digital (33, 62, 874)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3262, 874, F32, 29) (dual of [874, 812, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3262, 1042, F32, 29) (dual of [1042, 980, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,11]) [i] based on
- linear OA(3257, 1025, F32, 29) (dual of [1025, 968, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(3245, 1025, F32, 23) (dual of [1025, 980, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to C([0,14]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3262, 1042, F32, 29) (dual of [1042, 980, 30]-code), using
(62−29, 62, 705091)-Net in Base 32 — Upper bound on s
There is no (33, 62, 705092)-net in base 32, because
- 1 times m-reduction [i] would yield (33, 61, 705092)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 65 186299 343133 102765 650706 763584 880992 470015 944836 009322 025249 518614 589360 614607 672001 814672 > 3261 [i]