MinT - Best Known (173−93, 173, s)-Nets in Base 4

Best Known (173−93, 173, s)-Nets in Base 4

(173−93, 173, 104)-Net over F₄ — Constructive and digital

Digital (80, 173, 104)-net over F₄, using

t-expansion [i] based on digital (73, 173, 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]

(173−93, 173, 112)-Net over F₄ — Digital

Digital (80, 173, 112)-net over F₄, using

t-expansion [i] based on digital (73, 173, 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]

(173−93, 173, 1032)-Net in Base 4 — Upper bound on s

There is no (80, 173, 1033)-net in base 4, because

1 times m-reduction [i] would yield (80, 172, 1033)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 714329 416240 867746 447005 114766 876618 911474 310684 559065 251875 608543 249948 912426 329051 257016 694293 624320 > 4¹⁷² [i]