Best Known (40, 40+33, s)-Nets in Base 32
(40, 40+33, 240)-Net over F32 — Constructive and digital
Digital (40, 73, 240)-net over F32, using
- 3 times m-reduction [i] based on digital (40, 76, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 29, 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 (11, 47, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 29, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(40, 40+33, 327)-Net in Base 32 — Constructive
(40, 73, 327)-net in base 32, using
- 321 times duplication [i] based on (39, 72, 327)-net in base 32, using
- (u, u+v)-construction [i] based on
- (8, 24, 150)-net in base 32, using
- base change [i] based on (4, 20, 150)-net in base 64, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on (4, 20, 150)-net in base 64, using
- (15, 48, 177)-net in base 32, using
- base change [i] based on digital (7, 40, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 40, 177)-net over F64, using
- (8, 24, 150)-net in base 32, using
- (u, u+v)-construction [i] based on
(40, 40+33, 1171)-Net over F32 — Digital
Digital (40, 73, 1171)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3273, 1171, F32, 33) (dual of [1171, 1098, 34]-code), using
- 137 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 35 times 0, 1, 65 times 0) [i] based on linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- 137 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 35 times 0, 1, 65 times 0) [i] based on linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using
(40, 40+33, 1301215)-Net in Base 32 — Upper bound on s
There is no (40, 73, 1301216)-net in base 32, because
- 1 times m-reduction [i] would yield (40, 72, 1301216)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 348554 440763 228857 090715 869755 974853 866845 030367 535749 771683 261346 833880 128425 933140 190413 503747 066079 480671 > 3272 [i]