Best Known (110, 110+21, s)-Nets in Base 4
(110, 110+21, 6558)-Net over F4 — Constructive and digital
Digital (110, 131, 6558)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (100, 121, 6553)-net over F4, using
- net defined by OOA [i] based on linear OOA(4121, 6553, F4, 21, 21) (dual of [(6553, 21), 137492, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4121, 65531, F4, 21) (dual of [65531, 65410, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4121, 65531, F4, 21) (dual of [65531, 65410, 22]-code), using
- net defined by OOA [i] based on linear OOA(4121, 6553, F4, 21, 21) (dual of [(6553, 21), 137492, 22]-NRT-code), using
- digital (0, 10, 5)-net over F4, using
(110, 110+21, 34775)-Net over F4 — Digital
Digital (110, 131, 34775)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4131, 34775, F4, 21) (dual of [34775, 34644, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4131, 65547, F4, 21) (dual of [65547, 65416, 22]-code), using
- (u, u+v)-construction [i] based on
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4131, 65547, F4, 21) (dual of [65547, 65416, 22]-code), using
(110, 110+21, large)-Net in Base 4 — Upper bound on s
There is no (110, 131, large)-net in base 4, because
- 19 times m-reduction [i] would yield (110, 112, large)-net in base 4, but