Best Known (110, 132, s)-Nets in Base 5
(110, 132, 7112)-Net over F5 — Constructive and digital
Digital (110, 132, 7112)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (98, 120, 7102)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 7102, F5, 22, 22) (dual of [(7102, 22), 156124, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5120, 78122, F5, 22) (dual of [78122, 78002, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(5120, 78122, F5, 22) (dual of [78122, 78002, 23]-code), using
- net defined by OOA [i] based on linear OOA(5120, 7102, F5, 22, 22) (dual of [(7102, 22), 156124, 23]-NRT-code), using
- digital (1, 12, 10)-net over F5, using
(110, 132, 78174)-Net over F5 — Digital
Digital (110, 132, 78174)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5132, 78174, F5, 22) (dual of [78174, 78042, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5129, 78171, F5, 20) (dual of [78171, 78042, 21]-code), using Gilbert–Varšamov bound and bm = 5129 > Vbs−1(k−1) = 2093 551392 438519 134033 978849 958649 341280 527566 061387 058850 326452 192060 758815 302799 882169 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code), using
- construction X with Varšamov bound [i] based on
(110, 132, large)-Net in Base 5 — Upper bound on s
There is no (110, 132, large)-net in base 5, because
- 20 times m-reduction [i] would yield (110, 112, large)-net in base 5, but