Best Known (144, 144+26, s)-Nets in Base 4
(144, 144+26, 5056)-Net over F4 — Constructive and digital
Digital (144, 170, 5056)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-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 (4, 17, 15)-net over F4, using
(144, 144+26, 56702)-Net over F4 — Digital
Digital (144, 170, 56702)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4170, 56702, F4, 26) (dual of [56702, 56532, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4170, 65554, F4, 26) (dual of [65554, 65384, 27]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(49, 9, F4, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,4)), using
- 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(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4170, 65554, F4, 26) (dual of [65554, 65384, 27]-code), using
(144, 144+26, large)-Net in Base 4 — Upper bound on s
There is no (144, 170, large)-net in base 4, because
- 24 times m-reduction [i] would yield (144, 146, large)-net in base 4, but