Best Known (167−18, 167, s)-Nets in Base 4
(167−18, 167, 932076)-Net over F4 — Constructive and digital
Digital (149, 167, 932076)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (139, 157, 932067)-net over F4, using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- digital (1, 10, 9)-net over F4, using
(167−18, 167, 4194310)-Net over F4 — Digital
Digital (149, 167, 4194310)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4167, 4194310, F4, 2, 18) (dual of [(4194310, 2), 8388453, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(410, 9, F4, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- linear OOA(4157, 4194301, F4, 2, 18) (dual of [(4194301, 2), 8388445, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-code), using
- linear OOA(410, 9, F4, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(167−18, 167, large)-Net in Base 4 — Upper bound on s
There is no (149, 167, large)-net in base 4, because
- 16 times m-reduction [i] would yield (149, 151, large)-net in base 4, but