MinT - Best Known (235−155, 235, s)-Nets in Base 4

Best Known (235−155, 235, s)-Nets in Base 4

(235−155, 235, 104)-Net over F₄ — Constructive and digital

Digital (80, 235, 104)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(235−155, 235, 112)-Net over F₄ — Digital

Digital (80, 235, 112)-net over F₄, using

t-expansion [i] based on digital (73, 235, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(235−155, 235, 602)-Net in Base 4 — Upper bound on s

There is no (80, 235, 603)-net in base 4, because

1 times m-reduction [i] would yield (80, 234, 603)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 805 429600 484779 422421 444395 508730 831472 980402 149171 940886 167373 878710 189277 973070 867929 148616 552890 006534 080247 147014 062267 736645 336094 858168 > 4²³⁴ [i]