MinT - Best Known (230−157, 230, s)-Nets in Base 4

Best Known (230−157, 230, s)-Nets in Base 4

(230−157, 230, 104)-Net over F₄ — Constructive and digital

Digital (73, 230, 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]

(230−157, 230, 112)-Net over F₄ — Digital

Digital (73, 230, 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]

(230−157, 230, 520)-Net in Base 4 — Upper bound on s

There is no (73, 230, 521)-net in base 4, because

1 times m-reduction [i] would yield (73, 229, 521)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 757305 877906 654872 927923 720596 793863 472809 411608 474804 917743 384626 073462 424323 126139 404513 100477 588117 273657 189636 851481 177353 802307 202816 > 4²²⁹ [i]