Best Known (107, 107+10, s)-Nets in Base 4
(107, 107+10, 6710885)-Net over F4 — Constructive and digital
Digital (107, 117, 6710885)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- a shift-net [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (102, 112, 6710880)-net over F4, using
- trace code for nets [i] based on digital (18, 28, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- trace code for nets [i] based on digital (18, 28, 1677720)-net over F256, using
- digital (0, 5, 5)-net over F4, using
(107, 107+10, large)-Net over F4 — Digital
Digital (107, 117, large)-net over F4, using
- 43 times duplication [i] based on digital (104, 114, large)-net over F4, using
- t-expansion [i] based on digital (102, 114, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4114, large, F4, 12) (dual of [large, large−114, 13]-code), using
- 6 times code embedding in larger space [i] based on linear OA(4108, large, F4, 12) (dual of [large, large−108, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 6 times code embedding in larger space [i] based on linear OA(4108, large, F4, 12) (dual of [large, large−108, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4114, large, F4, 12) (dual of [large, large−114, 13]-code), using
- t-expansion [i] based on digital (102, 114, large)-net over F4, using
(107, 107+10, large)-Net in Base 4 — Upper bound on s
There is no (107, 117, large)-net in base 4, because
- 8 times m-reduction [i] would yield (107, 109, large)-net in base 4, but