Best Known (26, 42, s)-Nets in Base 128
(26, 42, 2240)-Net over F128 — Constructive and digital
Digital (26, 42, 2240)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (15, 31, 2048)-net over F128, using
- net defined by OOA [i] based on linear OOA(12831, 2048, F128, 16, 16) (dual of [(2048, 16), 32737, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using
- net defined by OOA [i] based on linear OOA(12831, 2048, F128, 16, 16) (dual of [(2048, 16), 32737, 17]-NRT-code), using
- digital (3, 11, 192)-net over F128, using
(26, 42, 8194)-Net in Base 128 — Constructive
(26, 42, 8194)-net in base 128, using
- net defined by OOA [i] based on OOA(12842, 8194, S128, 16, 16), using
- OA 8-folding and stacking [i] based on OA(12842, 65552, S128, 16), using
- discarding factors based on OA(12842, 65553, S128, 16), using
- discarding parts of the base [i] based on linear OA(25636, 65553, F256, 16) (dual of [65553, 65517, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(25636, 65553, F256, 16) (dual of [65553, 65517, 17]-code), using
- discarding factors based on OA(12842, 65553, S128, 16), using
- OA 8-folding and stacking [i] based on OA(12842, 65552, S128, 16), using
(26, 42, 40201)-Net over F128 — Digital
Digital (26, 42, 40201)-net over F128, using
(26, 42, large)-Net in Base 128 — Upper bound on s
There is no (26, 42, large)-net in base 128, because
- 14 times m-reduction [i] would yield (26, 28, large)-net in base 128, but