MinT - Best Known (234−142, 234, s)-Nets in Base 4

Best Known (234−142, 234, s)-Nets in Base 4

(234−142, 234, 104)-Net over F₄ — Constructive and digital

Digital (92, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(234−142, 234, 144)-Net over F₄ — Digital

Digital (92, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(234−142, 234, 819)-Net in Base 4 — Upper bound on s

There is no (92, 234, 820)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 806 583038 984338 747265 145770 370215 820220 344827 623268 821519 686534 899454 777249 867016 646241 173935 030379 903226 764002 822478 141782 545481 607604 455152 > 4²³⁴ [i]