MinT - Best Known (186−110, 186, s)-Nets in Base 4

Best Known (186−110, 186, s)-Nets in Base 4

(186−110, 186, 104)-Net over F₄ — Constructive and digital

Digital (76, 186, 104)-net over F₄, using

t-expansion [i] based on digital (73, 186, 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]

(186−110, 186, 112)-Net over F₄ — Digital

Digital (76, 186, 112)-net over F₄, using

t-expansion [i] based on digital (73, 186, 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]

(186−110, 186, 728)-Net in Base 4 — Upper bound on s

There is no (76, 186, 729)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9967 898214 808226 874751 215045 014140 788419 967496 953009 817617 892675 238257 808334 421894 876324 009372 636713 069117 561424 > 4¹⁸⁶ [i]