Best Known (104, 120, s)-Nets in Base 5
(104, 120, 244156)-Net over F5 — Constructive and digital
Digital (104, 120, 244156)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-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 (3, 11, 16)-net over F5, using
(104, 120, 1320200)-Net over F5 — Digital
Digital (104, 120, 1320200)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5120, 1320200, F5, 16) (dual of [1320200, 1320080, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 1953137, F5, 16) (dual of [1953137, 1953017, 17]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(55, 6, F5, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,5)), using
- dual of repetition code with length 6 [i]
- linear OA(56, 6, F5, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,5)), 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(55, 6, F5, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,5)), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(5120, 1953137, F5, 16) (dual of [1953137, 1953017, 17]-code), using
(104, 120, large)-Net in Base 5 — Upper bound on s
There is no (104, 120, large)-net in base 5, because
- 14 times m-reduction [i] would yield (104, 106, large)-net in base 5, but