Best Known (77−28, 77, s)-Nets in Base 32
(77−28, 77, 320)-Net over F32 — Constructive and digital
Digital (49, 77, 320)-net over F32, using
- 1 times m-reduction [i] based on digital (49, 78, 320)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 7, 64)-net over F32, using
- s-reduction based on digital (2, 7, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- s-reduction based on digital (2, 7, 496)-net over F32, using
- digital (3, 10, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (3, 12, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 17, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 32, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (2, 7, 64)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(77−28, 77, 1170)-Net in Base 32 — Constructive
(49, 77, 1170)-net in base 32, using
- base change [i] based on digital (27, 55, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
(77−28, 77, 6924)-Net over F32 — Digital
Digital (49, 77, 6924)-net over F32, using
(77−28, 77, large)-Net in Base 32 — Upper bound on s
There is no (49, 77, large)-net in base 32, because
- 26 times m-reduction [i] would yield (49, 51, large)-net in base 32, but