Best Known (97−49, 97, s)-Nets in Base 4
(97−49, 97, 57)-Net over F4 — Constructive and digital
Digital (48, 97, 57)-net over F4, using
- 1 times m-reduction [i] based on digital (48, 98, 57)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 35, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (13, 63, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- digital (10, 35, 27)-net over F4, using
- (u, u+v)-construction [i] based on
(97−49, 97, 65)-Net in Base 4 — Constructive
(48, 97, 65)-net in base 4, using
- 5 times m-reduction [i] based on (48, 102, 65)-net in base 4, using
- base change [i] based on digital (14, 68, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- base change [i] based on digital (14, 68, 65)-net over F8, using
(97−49, 97, 81)-Net over F4 — Digital
Digital (48, 97, 81)-net over F4, using
- t-expansion [i] based on digital (46, 97, 81)-net over F4, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 46 and N(F) ≥ 81, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
(97−49, 97, 817)-Net in Base 4 — Upper bound on s
There is no (48, 97, 818)-net in base 4, because
- 1 times m-reduction [i] would yield (48, 96, 818)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 6422 239813 650435 834740 766831 124162 547265 615774 919989 221404 > 496 [i]