Best Known (74, 74+131, s)-Nets in Base 4
(74, 74+131, 104)-Net over F4 — Constructive and digital
Digital (74, 205, 104)-net over F4, using
- t-expansion [i] based on digital (73, 205, 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
(74, 74+131, 112)-Net over F4 — Digital
Digital (74, 205, 112)-net over F4, using
- t-expansion [i] based on digital (73, 205, 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
(74, 74+131, 595)-Net in Base 4 — Upper bound on s
There is no (74, 205, 596)-net in base 4, because
- 1 times m-reduction [i] would yield (74, 204, 596)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 709 034267 173922 480469 673709 973300 592628 983295 535528 585155 225572 607213 480071 041735 394442 992563 783382 900542 931697 982022 089265 > 4204 [i]