Best Known (103, 119, s)-Nets in Base 5
(103, 119, 244152)-Net over F5 — Constructive and digital
Digital (103, 119, 244152)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 12)-net over F5, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- digital (93, 109, 244140)-net over F5, using
- net defined by OOA [i] based on linear OOA(5109, 244140, F5, 16, 16) (dual of [(244140, 16), 3906131, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5109, 1953120, F5, 16) (dual of [1953120, 1953011, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(5109, 1953120, F5, 16) (dual of [1953120, 1953011, 17]-code), using
- net defined by OOA [i] based on linear OOA(5109, 244140, F5, 16, 16) (dual of [(244140, 16), 3906131, 17]-NRT-code), using
- digital (2, 10, 12)-net over F5, using
(103, 119, 1176828)-Net over F5 — Digital
Digital (103, 119, 1176828)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5119, 1176828, F5, 16) (dual of [1176828, 1176709, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5119, 1953138, F5, 16) (dual of [1953138, 1953019, 17]-code), using
- (u, u+v)-construction [i] based on
- linear OA(510, 13, F5, 8) (dual of [13, 3, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(510, 15, F5, 8) (dual of [15, 5, 9]-code), using
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(510, 13, F5, 8) (dual of [13, 3, 9]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(5119, 1953138, F5, 16) (dual of [1953138, 1953019, 17]-code), using
(103, 119, large)-Net in Base 5 — Upper bound on s
There is no (103, 119, large)-net in base 5, because
- 14 times m-reduction [i] would yield (103, 105, large)-net in base 5, but