Best Known (151, 175, s)-Nets in Base 4
(151, 175, 21854)-Net over F4 — Constructive and digital
Digital (151, 175, 21854)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (138, 162, 21845)-net over F4, using
- net defined by OOA [i] based on linear OOA(4162, 21845, F4, 24, 24) (dual of [(21845, 24), 524118, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4162, 262140, F4, 24) (dual of [262140, 261978, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 262144, F4, 24) (dual of [262144, 261982, 25]-code), using
- 1 times truncation [i] based on linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 262144, F4, 24) (dual of [262144, 261982, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4162, 262140, F4, 24) (dual of [262140, 261978, 25]-code), using
- net defined by OOA [i] based on linear OOA(4162, 21845, F4, 24, 24) (dual of [(21845, 24), 524118, 25]-NRT-code), using
- digital (1, 13, 9)-net over F4, using
(151, 175, 174356)-Net over F4 — Digital
Digital (151, 175, 174356)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4175, 174356, F4, 24) (dual of [174356, 174181, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4175, 262201, F4, 24) (dual of [262201, 262026, 25]-code), using
- 1 times truncation [i] based on linear OA(4176, 262202, F4, 25) (dual of [262202, 262026, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(413, 58, F4, 6) (dual of [58, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- 1 times truncation [i] based on linear OA(4176, 262202, F4, 25) (dual of [262202, 262026, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4175, 262201, F4, 24) (dual of [262201, 262026, 25]-code), using
(151, 175, large)-Net in Base 4 — Upper bound on s
There is no (151, 175, large)-net in base 4, because
- 22 times m-reduction [i] would yield (151, 153, large)-net in base 4, but