Best Known (16, 16+18, s)-Nets in Base 32
(16, 16+18, 131)-Net over F32 — Constructive and digital
Digital (16, 34, 131)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (7, 25, 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 (0, 9, 33)-net over F32, using
(16, 16+18, 259)-Net in Base 32 — Constructive
(16, 34, 259)-net in base 32, using
- 2 times m-reduction [i] based on (16, 36, 259)-net in base 32, using
- base change [i] based on (10, 30, 259)-net in base 64, using
- 2 times m-reduction [i] based on (10, 32, 259)-net in base 64, using
- base change [i] based on digital (2, 24, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 24, 259)-net over F256, using
- 2 times m-reduction [i] based on (10, 32, 259)-net in base 64, using
- base change [i] based on (10, 30, 259)-net in base 64, using
(16, 16+18, 272)-Net over F32 — Digital
Digital (16, 34, 272)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3234, 272, F32, 18) (dual of [272, 238, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3234, 341, F32, 18) (dual of [341, 307, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3234, 341, F32, 18) (dual of [341, 307, 19]-code), using
(16, 16+18, 321)-Net in Base 32
(16, 34, 321)-net in base 32, using
- 2 times m-reduction [i] based on (16, 36, 321)-net in base 32, using
- base change [i] based on (10, 30, 321)-net in base 64, using
- 2 times m-reduction [i] based on (10, 32, 321)-net in base 64, using
- base change [i] based on digital (2, 24, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 24, 321)-net over F256, using
- 2 times m-reduction [i] based on (10, 32, 321)-net in base 64, using
- base change [i] based on (10, 30, 321)-net in base 64, using
(16, 16+18, 64935)-Net in Base 32 — Upper bound on s
There is no (16, 34, 64936)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1496 649965 911524 371946 284099 318589 527486 366453 537204 > 3234 [i]