Best Known (27, 27+8, s)-Nets in Base 32
(27, 27+8, 262641)-Net over F32 — Constructive and digital
Digital (27, 35, 262641)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- 1 times truncation [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- digital (21, 29, 262145)-net over F32, using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 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(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- digital (2, 6, 496)-net over F32, using
(27, 27+8, 2097150)-Net in Base 32 — Constructive
(27, 35, 2097150)-net in base 32, using
- net defined by OOA [i] based on OOA(3235, 2097150, S32, 8, 8), using
- OA 4-folding and stacking [i] based on OA(3235, 8388600, S32, 8), using
- discarding factors based on OA(3235, large, S32, 8), using
- discarding parts of the base [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding parts of the base [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- discarding factors based on OA(3235, large, S32, 8), using
- OA 4-folding and stacking [i] based on OA(3235, 8388600, S32, 8), using
(27, 27+8, 3658535)-Net over F32 — Digital
Digital (27, 35, 3658535)-net over F32, using
(27, 27+8, 4194301)-Net in Base 32
(27, 35, 4194301)-net in base 32, using
- net defined by OOA [i] based on OOA(3235, 4194301, S32, 10, 8), using
- OOA 2-folding and stacking with additional row [i] based on OOA(3235, large, S32, 2, 8), using
- discarding parts of the base [i] based on linear OOA(6429, large, F64, 2, 8), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- discarding parts of the base [i] based on linear OOA(6429, large, F64, 2, 8), using
- OOA 2-folding and stacking with additional row [i] based on OOA(3235, large, S32, 2, 8), using
(27, 27+8, large)-Net in Base 32 — Upper bound on s
There is no (27, 35, large)-net in base 32, because
- 6 times m-reduction [i] would yield (27, 29, large)-net in base 32, but