MinT - Best Known (103, 103+135, s)-Nets in Base 4

Best Known (103, 103+135, s)-Nets in Base 4

(103, 103+135, 104)-Net over F₄ — Constructive and digital

Digital (103, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(103, 103+135, 144)-Net over F₄ — Digital

Digital (103, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 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]

(103, 103+135, 1104)-Net in Base 4 — Upper bound on s

There is no (103, 238, 1105)-net in base 4, because

1 times m-reduction [i] would yield (103, 237, 1105)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50996 798284 279660 778738 237378 170071 172036 033225 756970 129435 618167 333741 959157 751287 743781 535596 822903 181336 871596 622947 103563 542753 577058 532144 > 4²³⁷ [i]