Best Known (105, 120, s)-Nets in Base 4
(105, 120, 149808)-Net over F4 — Constructive and digital
Digital (105, 120, 149808)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (97, 112, 149799)-net over F4, using
- net defined by OOA [i] based on linear OOA(4112, 149799, F4, 15, 15) (dual of [(149799, 15), 2246873, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4112, 1048594, F4, 15) (dual of [1048594, 1048482, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4112, 1048597, F4, 15) (dual of [1048597, 1048485, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4112, 1048597, F4, 15) (dual of [1048597, 1048485, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4112, 1048594, F4, 15) (dual of [1048594, 1048482, 16]-code), using
- net defined by OOA [i] based on linear OOA(4112, 149799, F4, 15, 15) (dual of [(149799, 15), 2246873, 16]-NRT-code), using
- digital (1, 8, 9)-net over F4, using
(105, 120, 612975)-Net over F4 — Digital
Digital (105, 120, 612975)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4120, 612975, F4, 15) (dual of [612975, 612855, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4120, 1048593, F4, 15) (dual of [1048593, 1048473, 16]-code), using
- (u, u+v)-construction [i] based on
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4120, 1048593, F4, 15) (dual of [1048593, 1048473, 16]-code), using
(105, 120, large)-Net in Base 4 — Upper bound on s
There is no (105, 120, large)-net in base 4, because
- 13 times m-reduction [i] would yield (105, 107, large)-net in base 4, but