Best Known (19, 19+21, s)-Nets in Base 32
(19, 19+21, 142)-Net over F32 — Constructive and digital
Digital (19, 40, 142)-net over F32, using
- 1 times m-reduction [i] based on digital (19, 41, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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
- digital (7, 29, 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 (1, 12, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(19, 19+21, 261)-Net in Base 32 — Constructive
(19, 40, 261)-net in base 32, using
- base change [i] based on digital (4, 25, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(19, 19+21, 306)-Net over F32 — Digital
Digital (19, 40, 306)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3240, 306, F32, 21) (dual of [306, 266, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 341, F32, 21) (dual of [341, 301, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3240, 341, F32, 21) (dual of [341, 301, 22]-code), using
(19, 19+21, 321)-Net in Base 32
(19, 40, 321)-net in base 32, using
- t-expansion [i] based on (18, 40, 321)-net in base 32, using
- 2 times m-reduction [i] based on (18, 42, 321)-net in base 32, using
- base change [i] based on (11, 35, 321)-net in base 64, using
- 1 times m-reduction [i] based on (11, 36, 321)-net in base 64, using
- base change [i] based on digital (2, 27, 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, 27, 321)-net over F256, using
- 1 times m-reduction [i] based on (11, 36, 321)-net in base 64, using
- base change [i] based on (11, 35, 321)-net in base 64, using
- 2 times m-reduction [i] based on (18, 42, 321)-net in base 32, using
(19, 19+21, 108312)-Net in Base 32 — Upper bound on s
There is no (19, 40, 108313)-net in base 32, because
- 1 times m-reduction [i] would yield (19, 39, 108313)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 50217 271859 404759 943221 744125 139538 121834 344304 788772 668328 > 3239 [i]