MinT - Best Known (103, 103+157, s)-Nets in Base 4

Best Known (103, 103+157, s)-Nets in Base 4

(103, 103+157, 104)-Net over F₄ — Constructive and digital

Digital (103, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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+157, 144)-Net over F₄ — Digital

Digital (103, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 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+157, 930)-Net in Base 4 — Upper bound on s

There is no (103, 260, 931)-net in base 4, because

1 times m-reduction [i] would yield (103, 259, 931)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 903821 189568 468258 915904 209178 328718 876968 331329 679695 303775 342668 281291 230470 405089 816807 399509 923431 884087 318356 795690 052851 522491 506814 859685 238993 851760 > 4²⁵⁹ [i]