Best Known (46, 117, s)-Nets in Base 4
(46, 117, 56)-Net over F4 — Constructive and digital
Digital (46, 117, 56)-net over F4, using
- t-expansion [i] based on digital (33, 117, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(46, 117, 81)-Net over F4 — Digital
Digital (46, 117, 81)-net over F4, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 46 and N(F) ≥ 81, using
(46, 117, 430)-Net in Base 4 — Upper bound on s
There is no (46, 117, 431)-net in base 4, because
- 1 times m-reduction [i] would yield (46, 116, 431)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7054 948494 509222 552444 478758 751086 082127 541833 500968 008714 411591 044520 > 4116 [i]