Best Known (80, 80+153, s)-Nets in Base 4
(80, 80+153, 104)-Net over F4 — Constructive and digital
Digital (80, 233, 104)-net over F4, using
- t-expansion [i] based on digital (73, 233, 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
(80, 80+153, 112)-Net over F4 — Digital
Digital (80, 233, 112)-net over F4, using
- t-expansion [i] based on digital (73, 233, 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
(80, 80+153, 607)-Net in Base 4 — Upper bound on s
There is no (80, 233, 608)-net in base 4, because
- 1 times m-reduction [i] would yield (80, 232, 608)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 50 429384 454918 305291 858738 933435 490061 224377 163384 787154 707406 810474 337643 070721 356555 796259 825660 359580 215147 193034 037801 259826 937689 148625 > 4232 [i]