Best Known (103, 103+16, s)-Nets in Base 2
(103, 103+16, 2052)-Net over F2 — Constructive and digital
Digital (103, 119, 2052)-net over F2, using
- t-expansion [i] based on digital (102, 119, 2052)-net over F2, using
- net defined by OOA [i] based on linear OOA(2119, 2052, F2, 17, 17) (dual of [(2052, 17), 34765, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2119, 16417, F2, 17) (dual of [16417, 16298, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2113, 16385, F2, 17) (dual of [16385, 16272, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(285, 16385, F2, 13) (dual of [16385, 16300, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(2119, 16417, F2, 17) (dual of [16417, 16298, 18]-code), using
- net defined by OOA [i] based on linear OOA(2119, 2052, F2, 17, 17) (dual of [(2052, 17), 34765, 18]-NRT-code), using
(103, 103+16, 4282)-Net over F2 — Digital
Digital (103, 119, 4282)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2119, 4282, F2, 3, 16) (dual of [(4282, 3), 12727, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 5473, F2, 3, 16) (dual of [(5473, 3), 16300, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2119, 16419, F2, 16) (dual of [16419, 16300, 17]-code), using
- 1 times truncation [i] based on linear OA(2120, 16420, F2, 17) (dual of [16420, 16300, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2113, 16385, F2, 17) (dual of [16385, 16272, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(285, 16385, F2, 13) (dual of [16385, 16300, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2120, 16420, F2, 17) (dual of [16420, 16300, 18]-code), using
- OOA 3-folding [i] based on linear OA(2119, 16419, F2, 16) (dual of [16419, 16300, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 5473, F2, 3, 16) (dual of [(5473, 3), 16300, 17]-NRT-code), using
(103, 103+16, 113101)-Net in Base 2 — Upper bound on s
There is no (103, 119, 113102)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 664653 025821 451095 880495 269188 545055 > 2119 [i]