Best Known (203−125, 203, s)-Nets in Base 4
(203−125, 203, 104)-Net over F4 — Constructive and digital
Digital (78, 203, 104)-net over F4, using
- t-expansion [i] based on digital (73, 203, 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
(203−125, 203, 112)-Net over F4 — Digital
Digital (78, 203, 112)-net over F4, using
- t-expansion [i] based on digital (73, 203, 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
(203−125, 203, 680)-Net in Base 4 — Upper bound on s
There is no (78, 203, 681)-net in base 4, because
- 1 times m-reduction [i] would yield (78, 202, 681)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 43 737509 875886 183395 166587 857245 307387 266762 357424 654940 541718 198399 348334 882618 819728 048224 934749 013472 225396 710555 774400 > 4202 [i]