Best Known (148, 246, s)-Nets in Base 4
(148, 246, 138)-Net over F4 — Constructive and digital
Digital (148, 246, 138)-net over F4, using
- 10 times m-reduction [i] based on digital (148, 256, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 75, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- digital (73, 181, 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
- digital (21, 75, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(148, 246, 140)-Net in Base 4 — Constructive
(148, 246, 140)-net in base 4, using
- (u, u+v)-construction [i] based on
- (26, 75, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- digital (73, 171, 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
- (26, 75, 36)-net in base 4, using
(148, 246, 356)-Net over F4 — Digital
Digital (148, 246, 356)-net over F4, using
(148, 246, 6670)-Net in Base 4 — Upper bound on s
There is no (148, 246, 6671)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12828 475437 209111 259610 521546 767846 623581 167462 334050 012318 047264 119492 444591 629077 581244 814716 789521 890495 828858 069193 869778 982330 114339 023731 420992 > 4246 [i]