Best Known (33, 33+28, s)-Nets in Base 32
(33, 33+28, 218)-Net over F32 — Constructive and digital
Digital (33, 61, 218)-net over F32, using
- 2 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
(33, 33+28, 301)-Net in Base 32 — Constructive
(33, 61, 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, 46, 257)-net in base 32, using
- 2 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
- 2 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- digital (1, 15, 44)-net over F32, using
(33, 33+28, 1000)-Net over F32 — Digital
Digital (33, 61, 1000)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3261, 1000, F32, 28) (dual of [1000, 939, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, 1044, F32, 28) (dual of [1044, 983, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(3255, 1024, F32, 28) (dual of [1024, 969, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3241, 1024, F32, 21) (dual of [1024, 983, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(326, 20, F32, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3261, 1044, F32, 28) (dual of [1044, 983, 29]-code), using
(33, 33+28, 705091)-Net in Base 32 — Upper bound on s
There is no (33, 61, 705092)-net in base 32, because
- 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]