Best Known (91−44, 91, s)-Nets in Base 32
(91−44, 91, 240)-Net over F32 — Constructive and digital
Digital (47, 91, 240)-net over F32, using
- 6 times m-reduction [i] based on digital (47, 97, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 36, 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, 61, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 36, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(91−44, 91, 513)-Net in Base 32 — Constructive
(47, 91, 513)-net in base 32, using
- t-expansion [i] based on (46, 91, 513)-net in base 32, using
- 17 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 17 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(91−44, 91, 875)-Net over F32 — Digital
Digital (47, 91, 875)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3291, 875, F32, 44) (dual of [875, 784, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, 1047, F32, 44) (dual of [1047, 956, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(35) [i] based on
- linear OA(3284, 1024, F32, 44) (dual of [1024, 940, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3268, 1024, F32, 36) (dual of [1024, 956, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(327, 23, F32, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(43) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(3291, 1047, F32, 44) (dual of [1047, 956, 45]-code), using
(91−44, 91, 491279)-Net in Base 32 — Upper bound on s
There is no (47, 91, 491280)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 93035 464837 121072 402199 785711 696823 680364 492259 056724 017359 126434 453515 041579 347249 967783 820031 968027 516530 234091 474552 777133 185460 973616 > 3291 [i]