Best Known (77, 241, s)-Nets in Base 4
(77, 241, 104)-Net over F4 — Constructive and digital
Digital (77, 241, 104)-net over F4, using
- t-expansion [i] based on digital (73, 241, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(77, 241, 112)-Net over F4 — Digital
Digital (77, 241, 112)-net over F4, using
- t-expansion [i] based on digital (73, 241, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(77, 241, 549)-Net in Base 4 — Upper bound on s
There is no (77, 241, 550)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13 883880 591797 840085 460986 231578 030695 118971 847047 055727 167334 580470 135355 857222 058773 758301 419499 488604 560441 008783 887134 179585 345204 515262 046368 > 4241 [i]