MinT - Best Known (77, 77+106, s)-Nets in Base 4

Best Known (77, 77+106, s)-Nets in Base 4

(77, 77+106, 104)-Net over F₄ — Constructive and digital

Digital (77, 183, 104)-net over F₄, using

t-expansion [i] based on digital (73, 183, 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]

(77, 77+106, 112)-Net over F₄ — Digital

Digital (77, 183, 112)-net over F₄, using

t-expansion [i] based on digital (73, 183, 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]

(77, 77+106, 780)-Net in Base 4 — Upper bound on s

There is no (77, 183, 781)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 156 751602 103463 884447 522862 026006 863076 674639 660989 468602 241873 727801 416342 694596 308978 381761 294875 579147 963200 > 4¹⁸³ [i]