Best Known (16, 33, s)-Nets in Base 32
(16, 33, 142)-Net over F32 — Constructive and digital
Digital (16, 33, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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, 24, 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, 9, 44)-net over F32, using
(16, 33, 260)-Net in Base 32 — Constructive
(16, 33, 260)-net in base 32, using
- 321 times duplication [i] based on (15, 32, 260)-net in base 32, using
- base change [i] based on digital (3, 20, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 20, 260)-net over F256, using
(16, 33, 413)-Net over F32 — Digital
Digital (16, 33, 413)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3233, 413, F32, 2, 17) (dual of [(413, 2), 793, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3233, 513, F32, 2, 17) (dual of [(513, 2), 993, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3233, 1026, F32, 17) (dual of [1026, 993, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3233, 1024, F32, 17) (dual of [1024, 991, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3231, 1024, F32, 16) (dual of [1024, 993, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3233, 1026, F32, 17) (dual of [1026, 993, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(3233, 513, F32, 2, 17) (dual of [(513, 2), 993, 18]-NRT-code), using
(16, 33, 127325)-Net in Base 32 — Upper bound on s
There is no (16, 33, 127326)-net in base 32, because
- 1 times m-reduction [i] would yield (16, 32, 127326)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 461545 491487 962149 784803 996107 491855 126319 287321 > 3232 [i]