Best Known (140, 140+26, s)-Nets in Base 4
(140, 140+26, 5046)-Net over F4 — Constructive and digital
Digital (140, 166, 5046)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (127, 153, 5041)-net over F4, using
- net defined by OOA [i] based on linear OOA(4153, 5041, F4, 26, 26) (dual of [(5041, 26), 130913, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4153, 65533, F4, 26) (dual of [65533, 65380, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4153, 65533, F4, 26) (dual of [65533, 65380, 27]-code), using
- net defined by OOA [i] based on linear OOA(4153, 5041, F4, 26, 26) (dual of [(5041, 26), 130913, 27]-NRT-code), using
- digital (0, 13, 5)-net over F4, using
(140, 140+26, 45001)-Net over F4 — Digital
Digital (140, 166, 45001)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4166, 45001, F4, 26) (dual of [45001, 44835, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 65550, F4, 26) (dual of [65550, 65384, 27]-code), using
- (u, u+v)-construction [i] based on
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- dual of repetition code with length 14 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4166, 65550, F4, 26) (dual of [65550, 65384, 27]-code), using
(140, 140+26, large)-Net in Base 4 — Upper bound on s
There is no (140, 166, large)-net in base 4, because
- 24 times m-reduction [i] would yield (140, 142, large)-net in base 4, but